weak convergence of the variations iterated integrals and doleans dade exponentials of sequences of semimartingales abstract this document investigates the weak convergence of variations iterated integrals and doleans dade exponentials v sub k y i sub k y and e gamma y are called respectively the variations the iterated integrals and the doleans dade exponential of the semimartingale y

transient behavior analysis of vibrationally controlled nonlinear parabolic systems with neumann boundary conditions the transient behavior of vibrationally controlled distributed parameter systems governed by parabolic partial differential equations pdes with neumann boundary conditions is analyzed the analysis uses a certain mapping and a time invariant pde whose trajectories under this mapping yield the approximate moving averages along the trajectories of the vibrationally controlled system this approach considerably enhances the understanding of the behavior of vibrationally controlled distributed parameter systems and facilitates a selection of the parameters of stabilizing vibrations that ensure transient behavior with more desirable properties

non trivial effect of fast vibration on the dynamics of a class of non linearly damped mechanical systems the effect of very high frequency excitation on the slow dynamics of a class of non linearly damped mechanical oscillators is considered two different models of damping namely piecewise linear and pth power damping are considered fast excitation is modelled as triangular sinusoidal and random base excitation the effect of fast excitation is theoretically analyzed using the method of direct partition of motion mdpm and direct simulation the method of numerical averaging is also used where damping characteristics or excitations are not amenable to analytical techniques fast excitation has the non trivial effect of increasing and decreasing the low velocity damping of hard and soft dampers respectively the effect of fast excitation on the transient and steady state slow dynamics of the system is investigated by direct numerical integration of the equation of motion

adaptive distributed parameter systems identification with enforceable identifiability conditions and reduced order spatial differentiation presents the synthesis of adaptive identifiers for distributed parameter systems dps with spatially varying parameters described by partial differential equations pdes of parabolic elliptic and hyperbolic type the features of the pde setting are utilized to obtain the not directly intuitive parameter estimation algorithms that use spatial derivatives of the output data with the order reduced from that of the highest spatial plant derivative the tunable identifier parameters are passed through the integrator block which forms their orthogonal expansions the latter are shown to be pointwise plant parameter estimates in this regard the approach of the paper is in the spirit of finite dimensional observer realization in integrating rather than differentiating the output data only applied to the spatial rather than temporal domain the constructively enforceable identifiability conditions formulated in terms of the sufficiently rich input signals referred to as generators of persistent excitation are shown to guarantee the existence of a unique zero steady state for the parameter errors under such inputs the tunable parameters in the adaptive identifiers proposed are shown to converge to plant parameters in l sub 2 and the orthogonal expansions of these tunable parameters pointwise

vibrational control of nonlinear systems vibrational stabilizability in this work the theory of vibrational control for nonlinear systems is developed the present paper gives criteria for stabilizability of nonlinear systems by linear multiplicative vibrations by almost periodic forcing and by vector additive vibrations illustrative examples are also considered in a subsequent paper the problem of vibrational controllability and transient behavior will be addressed

weak solutions of set valued stochastic differential equations abstract the paper is devoted to the existence of weak solutions of set valued stochastic differential equations such equations were considered in the authors paper 22 where existence and uniqueness of strong solutions have been investigated now apart from the existence of weak solutions the weak compactness in distribution of the set of all weak solutions of set valued stochastic differential equations is considered

asymptotic properties of monte carlo estimators of diffusion processes abstract this paper studies the limit distributions of monte carlo estimators of diffusion processes we examine two types of estimators based on the euler scheme one applied to the original processes the other to a doss transformation of the processes we show that the transformation increases the speed of convergence of the euler scheme we also study estimators of conditional expectations of diffusions after characterizing expected approximation errors we construct second order bias corrected estimators we also derive new convergence results for the mihlstein scheme illustrations of the results are provided in the context of simulation based estimation of diffusion processes

particle representations for measure valued population models models of populations in which a type or location represented by a point in a metric space e is associated with each individual in the population are considered a population process is neutral if the chances of an individual replicating or dying do not depend on its type measurevalued processes are obtained as infinite population limits for a large class of neutral population models and it is shown that these measure valued processes can be represented in terms of the total mass of the population and the de finetti measures associated with an e valued particle model

a countable representation of the fleming viot measure valued diffusion the fleming viot measure valued diffusion arises as the infinite population limit of various discrete genetic models with general type space the paper gives a countable construction of the process as the empirical measure carried by a certain interactive particle system this explicit representation facilitates the study of various properties of the fleming viot process the construction also carries versions of the familiar genealogical processes from population genetics in particular kingman s coalescent thus unifying the genealogical and measure valued approaches to the subject

asymptotic behavior of a nonlinear kirchhoff type equation with spring boundary conditions in this paper we consider the initial boundary value problem for a nonlinear kirchhoff type equation with the damping term and spring boundary conditions we establish the global existence and uniqueness of solutions to this problem in time and give an example and simulation to illustrate our results for the proof we use the faedo galerkin approximate method finally we study the asymptotic behavior of solutions and some of its simulation results results of this paper are able to apply industrial parts such as a typical model widely used to represent threads wires magnetic tapes belts band saws and so on

stability of fast periodic systems with time lags the stability criterion of r bellman et al 1985 for fast periodic linear systems is extended to systems with time delays applying the results of j hale 1966 the asymptotic stability criterion for a class of time lag systems is derived a comparison to a nondelay case is made and it is demonstrated that small delays can significantly affect the stability properties of this class of systems

approximation theorems for random permanents and associated stochastic processes the limit theorems for certain stochastic processes generated by permanents of random matrices of independent columns with exchangeable components are established the results are based on the martingale decomposition of a random permanent function similar to the one known for u statistics and on relating the components of this decomposition to some multiple stochastic integrals

numerical approximation of doubly reflected bsdes with jumps and rcll obstacles we study a discrete time approximation scheme for the solution of a doubly reflected backward stochastic differential equation dbbsde in short with jumps driven by a brownian motion and an independent compensated poisson process moreover we suppose that the obstacles are right continuous and left limited rcll processes with predictable and totally inaccessible jumps and satisfy mokobodski s condition our main contribution consists in the construction of an implementable numerical sheme based on two random binomial trees and the penalization method which is shown to converge to the solution of the dbbsde finally we illustrate the theoretical results with some numerical examples in the case of general jumps

direct adaptive control of parabolic systems algorithm synthesis and convergence and stability analysis this paper presents a model reference adaptive control of a class of distributed parameter systems described by linear n dimensional parabolic partial differential equations unknown parameters appearing in the system equation are either constant or spatially varying distributed sensing and actuation are assumed to be available adaptation laws are obtained by the lyapunov redesign method it is shown that the concept of persistency of excitation which guarantees the parameter error convergence to zero in finite dimensional adaptive systems in infinite dimensional adaptive systems should be investigated in relation to time variable spatial variable and also boundary conditions unlike the finite dimensional case in infinite dimensional adaptive systems even a constant input is shown to be persistently exciting in the sense that it guarantees the convergence of parameter errors to zero averaging theorems for two time scale systems which involve a finite dimensional slow system and an infinite dimensional fast system are developed the exponential stability of the adaptive system which is critical in finite dimensional adaptive control in terms of tolerating disturbances and unmodeled dynamics is shown by applying averaging

beta coalescents and continuous stable random trees coalescents with multiple collisions also known as a coalescents were introduced by pitman and sagitov in 1999 these processes describe the evolution of particles that undergo stochastic coagulation in such a way that several blocks can merge at the same time to form a single block in the case that the measure a is the beta 2 a a distribution they are also known to describe the genealogies of large populations where a single individual can produce a large number of offspring here we use a recent result of birkner et al to prove that beta coalescents can be embedded in continuous stable random trees about which much is known due to the recent progress of duquesne and le gall our proof is based on a construction of the donnelly kurtz lookdown process using continuous random trees which is of independent interest this produces a number of results concerning the small time behavior of beta coalescents most notably we recover an almost sure limit theorem of the present authors for the number of blocks at small times and give the multifractal spectrum corresponding to the emergence of blocks with atypical size also we are able to find exact asymptotics for sampling formulae corresponding to the site frequency spectrum and the allele frequency spectrum associated with mutations in the context of population genetics

vibration control of an euler bernoulli beam under unknown spatiotemporally varying disturbance in this article the vibration suppression of an euler bernoulli beam system is considered by using the adaptive boundary control technique the dynamics of the beam are represented by a partial differential equation and four ordinary differential equations involving functions of both space and time by using lyapunov synthesis the robust boundary control with a disturbance observer is first proposed to suppress the vibration and attenuate the effect of the external disturbances to compensate for both the system parametric uncertainties and the disturbances uncertainties the adaptive boundary control is developed with the proposed boundary control the state of the beam system is proven to be uniformly ultimately bounded and converge to a small neighbourhood of zero by appropriately choosing the design parameters the effectiveness of the proposed control is successfully verified by numerical simulations

syntax vs semantics a polarized approach we present a notion of sliced proof nets for the polarized fragment of linear logic and a corresponding game model we show that the connection between them is very strong through an equivalence of categories this contains soundness full completeness and faithful completeness

convergence in various topologies for stochastic integrals driven by semimartingales we generalize existing limit theory for stochastic integrals driven by semimartingales and with left continuous integrands joint skorohod convergence is replaced with joint finite dimensional convergence plus an assumption excluding the case when oscillations of the integrand appear immediately before oscillations of the integrator integrands may converge in a very weak topology it is also proved that convergence of integrators implies convergence of stochastic integrals with respect to the same topology

on the stability bifurcation of a nonlinear time delay system abstract a computational burden has always been associated with the stability analysis of a time delay system over its entire parameter ranges indeed this has led many previous investigators to develop control schemes under the assumption of small or negligible time delay in this paper we have attempted to explore an alternative approach which has been previously called as critical or single points hale s method projection series and centre manifold here we have deliberately omitted the relevant theorems lemmas or corollaries of this approach and rather focus mainly on a calculation spirit to make the underlying ideas accessible to investigators seeking more insight into the wealth of time delay dynamics the nonlinear delay equation around which we present this approach is a variational form of equations studied earlier by bentsman et al 1991 lehman et al 1992 and lehman and bentsman 1992 lehman and bentsman 1994 furthermore using the integral averaging method explicit bifurcation equations of the form g a 0 are derived and from the signs of their characteristic exponents the stability of the trivial and nontrivial solutions is obtained

application of vibrational control to linear quadratic control problems abstract the application of the theory of vibrational control to linear quadratic control problems is developed the solution of the matrix riccati differential equation rde and the optimal trajectory are found approximately as power series of a small parameter the minimizing effect of vibrations on the maximal solution of rde and the cost functional is studied the region of attraction of the maximal solution of rde for the case of hamiltonian matrix with imaginary axis eigenvalues is found special attention is paid to the application of vibrations to the linear quadratic problem of stabilization with respect to a part of variables and transfer of the other variables to a given position a problem of vibrational stabilization and optimal control of a carriage with an inverted pendulum is solved as an example

correlation free forms for nonlinear stochastic systems abstract an asymptotic method for analysis of nonlinear systems with wide band and high frequency stochastic perturbation is developed correlation free ito limiting equations are derived and a generalization of the wong zakai correction for the drift term is obtained a correction for the diffusion term is also shown to exist several illustrative examples are considered

convergence of filters with applications to the kalman bucy case for each n and each fixed time t a signal x sup n and a noisy observation y sup n are defined by a pair of stochastic difference equations under certain conditions x sup n y sup n converges in distribution to x y where dx t f t x t dt dv t dy t g t x t dt dw t conditions are found under which convergence in distribution of the conditional expectations e f x sup n mod y sup n to e f x mod y follows for every bounded continuous function f the case in which the conditional expectations still converge but the limit is not e f x mod y is also studied in the situation where f and g are linear functions of x an examination of this limit leads to a kalman bucy type estimate of x sup n which is asymptotically optimal and is an improvement on the usual kalman bucy estimate

vibrational feedback control of time delay systems this paper applies vibrational feedback control to time lag systems averaging theory for differential delay systems is presented and then applied to aid in the design of periodic controllers both stabilization and transient issues are discussed an illustrative example is given which demonstrates that the proposed controller 1 provides superior robustness properties in comparison to time invariant controllers when applied correctly 2 is not robust with respect to unmodeled delays and 3 does not have zero placement capabilities in the sense defined in the paper

a general storage theorem for integers in call by name l calculus the notion of storage operator introduced in j l krivine 1991 1990 appears to be an important tool in the study of data types in second order calculus these operators are terms which simulate call by value in the call by name strategy and they can be used in order to modelize assignment instructions the main result about storage operators is that there is a very simple second order type for them using godel s not not translation of classical into intuitionistic logic we give here a new and simpler proof of a strengthened version of this theorem which contains all previous result in intuitionistic and in classical logic j l krivine 1990 1992 and gives rise to new storage theorems moreover this result has a simple and intuitive meaning in terms of realizability

dependent choice quote and the clock in the proof program correspondence every axiom must be associated with an instruction we show that the axiom of dependent choice is associated with a clock instruction or a signature instruction

the tree length of an evolving coalescent a well established model for the genealogy of a large population in equilibrium is kingman s coalescent for the population together with its genealogy evolving in time this gives rise to a time stationary tree valued process we study the sum of the branch lengths briefly denoted as tree length and prove that the suitably compensated sequence of tree length processes converges as the population size tends to infinity to a limit process with cadlag paths infinite infinitesimal variance and a gumbel distribution as its equilibrium

some general effects of strong high frequency excitation stiffening biasing and smoothening abstract mechanical high frequency hf excitation provides a working principle behind many industrial and natural applications and phenomena this paper concerns three particular effects of hf excitation that may change the apparent characteristics of mechanical systems 1 stiffening by which the apparent linear stiffness associated with an equilibrium is changed along with derived quantities such as stability and natural frequencies 2 biasing by which the system is biased towards a particular state static or dynamic which does not exist or is unstable in the absence of the hf excitation and 3 smoothening referring to a tendency for discontinuities to be effectively smeared out by hf excitation illustrating first these effects for a few specific systems analytical results are provided that quantify them for a quite general class of mechanical systems this class covers systems that can be modelled by a finite number of second order ordinary differential equations generally non linear with periodically oscillating excitation terms of high frequency and small amplitude the results should be useful for understanding the effects in question in a broader perspective than is possible with specific systems for calculating effects for specific systems using well defined formulas and for possibly designing systems that display prescribed characteristics in the presence of hf excitation

condition of vibrational stabilizability for a class of nonlinear systems a notion of vibrational stabilizability for a class of nonlinear systems is introduced and analyzed

stochastic equations flows and measure valued processes we first prove some general results on pathwise uniqueness comparison property and existence of nonnegative strong solutions of stochastic equations driven by white noises and poisson random measures the results are then used to prove the strong existence of two classes of stochastic flows associated with coalescents with multiple collisions that is generalized fleming viot flows and flows of continuous state branching processes with immigration one of them unifies the different treatments of three kinds of flows in bertoin and le gall ann inst h poincare probab statist 41 2005 307 333 two scaling limit theorems for the generalized fleming viot flows are proved which lead to sub critical branching immigration superprocesses from those theorems we derive easily a generalization of the limit theorem for finite point motions of the flows in bertoin and le gall illinois j math 50 2006 147 181

differential equations driven by rough paths with jumps abstract we develop the rough path counterpart of ito stochastic integration and differential equations driven by general semimartingales this significantly enlarges the classes of ito forward stochastic differential equations treatable with pathwise methods a number of applications are discussed

smaller population size at the mrca time for stationary branching processes we consider an elementary model of random size varying population governed by a stationary continuous state branching process we compute the distributions of various variables related to the most recent common ancestor mrca the time to the mrca the size of the current population and the size of the population just before the mrca in particular we observe a natural mild bottleneck effect as the size of the population just before the mrca is stochastically smaller than the size of the current population we also compute the number of individuals involved in the last coalescent event of the genealogical tree that is the number of individuals at the time of the mrca who have descendants in the current population by studying more precisely the genealogical structure of the population we get asymptotics for the number of ancestors just before the current time we give explicit computations in the case of the quadratic branching mechanism in this case the size of the population at the mrca is in mean 2 3 of the size of the current population we also provide in this case the fluctuations for the renormalized number of ancestors

mutually catalytic branching in the plane finite measure states we study a pair of populations in r 2 which undergo diffusion and branching the system is interactive in that the branching rate of each type is proportional to the local density of the other type for a diffusion rate sufficiently large compared with the branching rate the model is constructed as the unique pair of finite measure valued processes which satisfy a martingale problem involving the collision local time of the solutions the processes are shown to have densities at fixed times which live on disjoint sets and explode as they approach the interface of the two populations in the long term limit global extinction of one type is shown the process constructed is a rescaled limit of the corresponding z 2 lattice model studied by d a dawson and e a perkins ann probab 26 1998 1088 1138 and resolves the large scale mass time space behavior of that model

optimal control of a co rotating vortex pair averaging and impulsive control abstract the problem of controlling the position of a pair of point vortices using a strain field or a field of a single source sink is considered the problem dimension is reduced by averaging over the fast rotation of vortices around the center of vorticity control is assumed to be function of rotation phase only for the case of the strain field actuation optimal control problem is posed in three different settings control input whose integral over a cycle of vortex rotation is bounded bounded control input and mixed problem where both integral over a cycle and control magnitude are bounded it is shown that optimal solutions in integral setting are impulsive they consist of dirac delta functions applied at optimal phases during the cycle of vortex rotation if a bound on the control magnitude is added to the constraints the mixed problem a solution is obtained for which control is at the maximum amplitude except possibly for intervals during which it is zero these results are obtained by direct optimization for the case of a source sink field we pose the optimal control problem of the averaged equations through the use of the pontryagin maximum principle an obtained solution is a set of dirac delta pulses at optimal phases of the vortex rotation cycle a discussion of these results in the context of vortex merger control is given impulsive control arises here naturally as an optimal control design once averaging method is used

convergence in probability for perturbed stochastic integral equations in this work one considers two stochastic integral equations indexed by some parameter and one studies the contiguity of their solutions when the parameter converges to some e0 two types of behaviour are described they lead to the notion of regular and singular perturbations the method which is used also enables a study of the rate of convergence applications to time discretization of equations are given

vibrational control without averaging the standard approach to vibrational control applies first order averaging methods to find an open loop periodic input that stabilizes an unstable equilibrium point while the capability of stabilization without feedback is appealing this formulation has drawbacks from a design perspective an alternative design framework based on stability maps for second order linear periodic systems is not as general but has significant potential advantages the averaging approach only guarantees that a solution exists the designer must then find that solution by other means furthermore the frequencies required may be too high for practical implementation use of stability maps makes a broader class of stabilizing inputs accessible allowing for example the use of lower frequency signals application to nonlinear and higher order systems is demonstrated with two examples the first is stabilization of the classical vertically forced inverted pendulum the second is delay of a pitchfork bifurcation in a fourth order nonlinear system in the second example we show that the averaging based approach necessarily fails to delay the bifurcation while the alternative method achieves significant extension of the stable operating region

inference in molecular population genetics full likelihood based inference for modern population genetics data presents methodological and computational challenges the problem is of considerable practical importance and has attracted recent attention with the development of algorithms based on importance sampling is and markov chain monte carlo mcmc sampling here we introduce a new is algorithm the optimal proposal distribution for these problems can be characterized and we exploit a detailed analysis of genealogical processes to develop a practicable approximation to it we compare the new method with existing algorithms on a variety of genetic examples our approach substantially outperforms existing is algorithms with efficiency typically improved by several orders of magnitude the new method also compares favourably with existing mcmc methods in some problems and less favourably in others suggesting that both is and mcmc methods have a continuing role to play in this area we offer insights into the relative advantages of each approach and we discuss diagnostics in the is framework

vibrational stabilization of linear time delay systems and its robustness with respect to the delay size abstract the purpose of this paper is to investigate the effectiveness of vibrational stabilization for a class of linear systems with time delay the total vibrational stabilizability conditions are formulated the robustness of an oscillatory stabilizing effect with respect to the magnitudes of the delays and the parameters of oscillations is also investigated on the basis of numerical examples

cost translation and a lifting approach to the multirate lqg problem it is shown how to translate an instance of a multirate sampled data lqg problem into an equivalent modified single rate shift invariant problem via a lifting isomorphism approach using this approach one can solve the multirate lqg problem without using periodic system theory or solving periodic riccati equations and without suffering any increases in state dimension this translation procedure shows the correct way to translate rms noise specification to the lifted domain for a multirate q design computer aided design package

martingale difference arrays and stochastic integrals consider mdas xni and yni and stopping times n t 0 t 1 denote s n t a 0 sum limits i 1 tau n t x ni text t n t b 0 sum limits i 1 tau n t y ni and let be a function if the common distribution converges and if st tt denote the corresponding limiting processes then we give conditions such that the martingale transforms sum limits i 1 tau n t varphi s n i 1 y ni converge weakly to the stochastic integral int limits 0 t varphi s dt this result has important consequences for functional central limit theorems 1 if the mdas are connected by a difference equation of the form x ni varphi left s n i 1 right y ni then weak convergence of tn t implies that of sn t and the limit satisfies the stochastic differential equation ds varphi left s right d t this observation leads to functional limit theorems for diffusion approximations e g we obtain easily a result of lindvall 4 on the diffusion approximation of branching processes 2 if the mda xni arises from a likelihood ratio martingale then the limit satisfies s t 1 int limits 0 t sdt which leads to the representation of the limiting likelihood ratios as exponential martingale s t exp t t frac 1 2 t t t this approximation by an exponential martingale has been proved previously by swensen 9 using a taylor expansion of the log likelihood ratio 3 as a consequence we obtain a general functional central limit theorem if left sum limits i 1 tau n t x ni 2 right converges weakly to s s t then left sum limits i 1 tau n t x ni right converges weakly to st provided that the distribution of st is uniquely determined by that of s s t this assertion embraces previous central limit theorems dealing with cases where the increasing process s s t is deterministic

vibrational control of systems with arrhenius dynamics abstract a nonlinear system with s shape steady state characteristic is referred to as a system with arrhenius dynamics the negative slope part of the s shape curve represents a set of unstable steady states using two examples of arrhenius systems catalytic reactor and continuous stirred tank reactor it is shown that introduction of sufficiently fast oscillations in the parameters of the system generates a new arrhenius system the steady state characteristic of which has a smaller negative slope part results of analytical investigation as well as numerical simulation are presented it is shown that vibrational stabilization of arrhenius systems gives an increase in productivity of the plants

vibrational control of nonlinear systems vibrational controllability and transient behavior in the first part of this work 1 the criteria for the existence of stabilizing parametric oscillations have been derived in the present paper the problem of choosing the stabilizing vibrations is addressed and the properties of transient behavior of vibrationally controlled nonlinear systems are analyzed

tree valued resampling dynamics martingale problems and applications the measure valued fleming viot process is a diffusion which models the evolution of allele frequencies in a multi type population in the neutral setting the kingman coalescent is known to generate the genealogies of the individuals in the population at a fixed time the goal of the present paper is to replace this static point of view on the genealogies by an analysis of the evolution of genealogies we encode the genealogy of the population as an isometry class of an ultra metric space which is equipped with a probability measure the space of ultra metric measure spaces together with the gromov weak topology serves as state space for tree valued processes we use well posed martingale problems to construct the tree valued resampling dynamics of the evolving genealogies for both the finite population moran model and the infinite population fleming viot diffusion we show that sufficient information about any ultra metric measure space is contained in the distribution of the vector of subtree lengths obtained by sequentially sampled individuals we give explicit formulas for the evolution of the laplace transform of the distribution of finite subtrees under the tree valued fleming viot dynamics

steady state behavior in the vibrational control of a class of nonlinear systems by ap forcing vibrational control is an open loop control technique that uses zero mean parametric vibrations for shaping the response of a linear or nonlinear dynamical system several theoretical results are available based on averaging techniques assuring the possibility of modifying the equilibrium properties of a system for nonlinear systems computational difficulties arise and theoretical results cannot easily be applied in this note the stationary behavior of a class of nonlinear systems vibrationally controlled by ap forcing is investigated a practical formula linking the amplitude and the frequency of the vibration and the amplitude of the steady state oscillation in the controlled variable is obtained as test cases the well known rayleigh equation a catalytic reactor equation and the phase locked loop equation are considered

convergence en loi des suites d integrales stochastiques sur l espace mathbb d 1 de skorokhod for sequences of stochastic integrals k n x n functional limit theorems are presented these results hold under simple natural conditions

semilinear elliptic equations with dirichlet operator and singular nonlinearities abstract in the paper we consider elliptic equations of the form a u u where a is the operator associated with a regular symmetric dirichlet form is a positive nontrivial measure and 0 we prove the existence and uniqueness of solutions of such equations as well as some regularity results we also study stability of solutions with respect to the convergence of measures on the right hand side of the equation for this purpose we introduce some type of functional convergence of smooth measures which in fact is equivalent to the quasi uniform convergence of associated potentials

a representation of exchangeable hierarchies by sampling from random real trees a hierarchy on a set s also called a total partition of s is a collection mathcal h of subsets of s such that s in mathcal h each singleton subset of s belongs to mathcal h and if a b in mathcal h then a cap b equals either a or b or varnothing every exchangeable random hierarchy of positive integers has the same distribution as a random hierarchy mathcal h associated as follows with a random real tree mathcal t equipped with root element 0 and a random probability distribution p on the borel subsets of mathcal t given mathcal t p let t 1 t 2 ldots be independent and identically distributed according to p and let mathcal h comprise all singleton subsets of mathbb n and every subset of the form j t j in f x as x ranges over mathcal t where f x is the fringe subtree of mathcal t rooted at x there is also the alternative characterization every exchangeable random hierarchy of positive integers has the same distribution as a random hierarchy mathcal h derived as follows from a random hierarchy mathscr h on 0 1 and a family u j of i i d uniform 0 1 random variables independent of mathscr h let mathcal h comprise all sets of the form j u j in b as b ranges over the members of mathscr h

robust adaptive boundary control of an axially moving string under a spatiotemporally varying tension in this paper a vibration suppression scheme for an axially moving string under a spatiotemporally varying tension and an unknown boundary disturbance is investigated the lower bound of the tension variation is assumed to be sufficiently larger than the derivatives of the tension the axially moving string system is divided into two spans i e a controlled span and an uncontrolled span by a hydraulic touch roll actuator which is located in the middle section of the string the transverse vibration of the controlled span part of the string is controlled by the hydraulic touch roll actuator and the position of the actuator is considered as the right boundary of the controlled span part the mathematical model of the system which consists of a hyperbolic partial differential equation describing the dynamics of the moving string and an ordinary differential equation describing the actuator dynamics is derived by using the hamilton s principle the lyapunov method is employed to design a robust boundary control law and adaptation laws for ensuring the vibration reduction of the controlled span part the asymptotic stability of the closed loop system under the robust adaptive boundary control scheme is proved through the use of semigroup theory simulation results verify the effectiveness of the robust adaptive boundary controller proposed

poisson representations of branching markov and measure valued branching processes representations of branching markov processes and their measure valued limits in terms of countable systems of particles are constructed for models with spatially varying birth and death rates each particle has a location and a level but unlike earlier constructions the levels change with time in fact death of a particle occurs only when the level of the particle crosses a specified level r or for the limiting models hits infinity for branching markov processes at each time t conditioned on the state of the process the levels are independent and uniformly distributed on 0 r for the limiting measure valued process at each time t the joint distribution of locations and levels is conditionally poisson distributed with mean measure k t x lambda where lambda denotes lebesgue measure and k is the desired measure valued process the representation simplifies or gives alternative proofs for a variety of calculations and results including conditioning on extinction or nonextinction harris s convergence theorem for supercritical branching processes and diffusion approximations for processes in random environments

cadlag skorokhod problem driven by a maximal monotone operator abstract the article deals with the existence and uniqueness of the solution of the following differential equation a cadlag skorokhod problem driven by a maximal monotone operator and with singular input generated by the cadlag function m d x t a x t d t d k t d d m t t 0 x 0 m 0 where k d is a pure jump function the jumps outside of the constrained domain d a are counteracted through the generalized projection by taking x t x t m t whenever x t m t d a approximations of the solution based on discretization and yosida penalization are also considered

vibrational control of a class of nonlinear systems by nonlinear multiplicative vibrations vibrational control is a nonclassical control principle which proposes a utilization of zero mean parametric excitation of a dynamical system for control purposes this paper extends nonlinear vibrational control theory developed in 8 9 to systems controlled by nonlinear multiplicative vibrations condition for partial vibrational stabilization with respect to a component of a steady state vector the choice of stabilizing vibrations and the transient motions are discussed for a certain practically important class of nonlinear vibrationally controlled systems the application of the results is demonstrated on the example of a catalytic reactor using a combination of numerical and analytical techniques

on the stationary distribution of the block counting process for population models with mutation and selection abstract we consider two population models subject to the evolutionary forces of selection and mutation the moran model and the wright fisher model in such models the block counting process traces back the number of potential ancestors of a sample of the population at present under some conditions the block counting process is positive recurrent and its stationary distribution is described via a linear system of equations in this work we first characterise the measures leading to a geometric stationary distribution the bolthausen sznitman model being the most prominent example having this feature next we solve the linear system of equations corresponding to the moran model for the wright fisher model we show that the probability generating function associated to the stationary distribution of the block counting process satisfies an integro differential equation we solve the latter for the kingman model and the star shaped model

fleming viot processes in population genetics fleming and viot indiana univ math j 28 1979 pp 817 843 introduced a class of probability measure valued diffusion processes that has attracted the interest of both pure and applied probabilists this paper surveys the subject of fleming viot processes as it relates to population genetics topics include 1 introduction 2 some measure valued markov chains 2 1 a diploid model 2 2 the wright fisher model 2 3 a moran model 3 the fleming viot process characterization 4 convergence 5 ergodicity 6 an infinite particle system 7 bounded mutation operators 8 reversibility 9 examples 9 1 continuous state stepwise mutation model 9 2 infinitely many neutral alleles model 9 3 infinitely many neutral alleles model with ages 9 4 two locus model with recombination 9 5 n locus model with gene conversion 9 6 infinitely many sites model without recombination 9 7 infinitely many neutral alleles model with allelic genealogies

getting results from programs extracted from classical proofs we present a new method to extract from a classical proof of x i x o y s x y a program computing y from x this method applies when o is a data type and s is a decidable predicate algorithms extracted this way are often far better than a stupid enumeration of all the possible outputs and this is verified on a nontrivial example a proof of dickson s lemma

a note on superprocesses subject to a mild restriction ona generator of the one particle motion we show thea fleming viot superprocess can be obtained from thea dawson watanabe superprocess by conditioning the latter to have constant total mass

robust adaptive control in hilbert space abstract though great advances have been reported in the field of adaptive control in the past decade some precise a priori structural information of the plant at least the order remains essential for most of the methods proposed this is unsatisfactory in some applications because of the unmodeled dynamics uncertain plant structure and the noisy operating environment in fact for many high performance control system designs for example control of large space structural systems the distributed nature of the plant must be taken into account these distributed parameter systems are frequently modelled by partial differential equations therefore they must be analyzed in the appropriate infinite dimensional state space a particular approach model reference adaptive control with command generator tracker concepts adopts a set of assumptions that are not system dimension dependent the method has been applied successfully to some finite dimensional systems and shows promise for the infinite dimensional state space generalization this paper elevates the theory from the finite dimensions to the finite dimensional hilbert space the key obstacles for such a transition are noted this then necessitates a modification of the adaptive control law under the modified scheme the error signal is shown driven to a residue set asymptotically the size of which depends on how close the nominal closed loop plant is to positive realness an added bonus is the robustness with respect to bounded state and output disturbances as well as model perturbation all these properties are not true in general for the finite dimensional control law the example of damped beam equation is included to illustrate the techniques

on line parameter estimation for infinite dimensional dynamical systems the on line or adaptive identification of parameters in abstract linear and nonlinear infinite dimensional dynamical systems is considered an estimator in the form of an infinite dimensional linear evolution system having the state and parameter estimates as its states is defined convergence of the state estimator is established via a lyapunov estimate the finite dimensional notion of a plant being sufficiently rich or persistently excited is extended to infinite dimensions convergence of the parameter estimates is established under the additional assumption that the plant is persistently excited a finite dimensional approximation theory is developed and convergence results are established numerical results for examples involving the estimation of both constant and functional parameters in one dimensional linear and nonlinear heat or diffusion equations and the estimation of stiffness and damping parameters in a one dimensional wave equation with kelvin voigt viscoelastic damping are presented

vss version of energy based control for swinging up a pendulum abstract a new algorithm ensuring global attractivity of the upright unstable equilibrium of a pendulum based on the variable structure system version of the energy speed gradient method is proposed it is shown that global attractivity cannot be obtained with continuous static state feedback a detailed global analysis of the transient behavior of the closed loop system is presented in addition it is shown that the global attractivity of the upright equilibrium can be achieved by applying a control of arbitrarily small magnitude

vibrational feedback control zeros placement capabilities it is shown that in addition to closed loop pole placement vibrational feedback controllers lead in the sense specified below to a possibility of open loop zeros assignability on this basis the superior performance characteristics of continuous time periodic controllers discovered in 3 6 are explained

smooth approximation of stochastic differential equations consider an ito process x satisfying the stochastic differential equation dx a x dt b x dw where a b are smooth and w is a multidimensional brownian motion suppose that wn has smooth sample paths and that wn converges weakly to w a central question in stochastic analysis is to understand the limiting behavior of solutions xn to the ordinary differential equation dxn a xn dt b xn dwn the classical wong zakai theorem gives sufficient conditions under which xn converges weakly to x provided that the stochastic integral b x dw is given the stratonovich interpretation the sufficient conditions are automatic in one dimension but in higher dimensions the correct interpretation of b x dw depends sensitively on how the smooth approximation wnis chosen in applications a natural class of smooth approximations arise by setting wn t n 1 2 nt0v sds where t is a flow generated e g by an ordinary differential equation and v is a mean zero observable under mild conditions on t we give a definitive answer to the interpretation question for the stochastic integral b x dw our theory applies to anosov or axiom a flows t as well as to a large class of nonuniformly hyperbolic flows including the one defined by the well known lorenz equations and our main results do not require any mixing assumptions on t the methods used in this paper are a combination of rough path theory and smooth ergodic theory

vibrational control of nonlinear time lag systems vibrational stabilization and transient behavior abstract this paper addresses two problems of control of nonlinear time lag systems i an existence and a synthesis of parametric vibrations for their stabilization and ii the transient behavior analysis of the vibrationally controlled nonlinear systems with time lags in this work stabilizability conditions for two vibration types are formulated and procedures for the synthesis of the corresponding stabilizing vibrations are proposed the method for the transient behavior analysis of vibrationally controlled systems on a finite time interval is developed as well several examples are given to support the theory presented

diffusion approximation for a class of transport processes with physical reflection boundary conditions consider a stochastic process consisting of the pair of a position and a velocity in a piecewise el d dimensional domain in the interior of the domain the dynamics are assigned by a potential and by random changes of the velocity occurring at exponentially distributed times according to a probability distribution which may depend on the current position and velocity on the boundary the process reflects physically the angle of reflection equals the angle of incidence first it is shown that the process is well defined for all times then when the coefficients depend on a diverging parameter n in particular such that the speed and the jump rate of the velocity go to xo with order rn and at least n respectively a diffusion approximation is sought the position process is represented as a solution of a skorohod reflection equation a skewing effect on the boundary results from the interaction between the dynamics and the reflection law so that the direction of reflection is in general oblique the assumption that the mean change of the velocity in the interior is linear in the current velocity up to order at least 1 2 in 1 n ensures that the cone of directions of reflection is independent of n the continuity properties of the skorohod oblique reflection problem enable one to show tightness of the position processes without having to estimate explicitly local times boundary layers and together with a suitable law of large numbers for the velocity allow one to identify the limit stochastic differential equation with oblique reflection the theory is illustrated by several applications in particular one to a mechanical model of brownian motion

when and how an error yields a dirichlet form we consider a random variable y and approximations yn n n defined on the same probability space with values in the same measurable space as y we are interested in situations where the approximations yn allow to define a dirichlet form in the space l2 py where py is the law of y our approach consists in studying both biases and variances the article attempts to propose a general theoretical framework it is illustrated by several examples

on the existence and uniqueness of solutions in adaptive control systems the issue of existence and uniqueness of solutions which arises in the analysis of adaptive control systems is investigated sufficient conditions that guarantee existence and uniqueness in positive time of solutions to differential equations describing a wide class of adaptive schemes are given the concept of filippov s solution is introduced as a method of dealing with discontinuous adaptive systems

on the persistence of excitation in the adaptive estimation of distributed parameter systems persistence of excitation is a sufficient condition for parameter convergence in adaptive identification schemes for dynamical systems for abstract parabolic and hyperbolic distributed parameter systems this condition requires that a family of bounded linear functionals be norm bounded away from zero the level of persistence of excitation of the plant and its implications are considered for a simple parabolic and hyperbolic system its effect on the qualitative and quantitative behavior of the estimators is investigated

high frequency nonlinear vibrational control this paper discusses the feasibility of high frequency nonlinear vibrational control such control has the advantage that it does not require state measurement and processing capabilities that are required in conventional feedback control bellman et al 1986 investigated nonlinear systems controlled by linear vibrational controllers and proved that vibrational control is not feasible if the jacobian matrix has a positive trace this paper extends previous work to include nonlinear vibrational controllers a stability criteria is derived for nonlinear systems with nonlinear controllers and it is shown that a nonlinear vibrational controller can stabilize a system even if the jacobian matrix has a positive trace

the genealogy of branching brownian motion with absorption we consider a system of particles which perform branching brownian motion with negative drift and are killed upon reaching zero in the near critical regime where the total population stays roughly constant with approximately n particles we show that the characteristic time scale for the evolution of this population is of order logn 3 in the sense that when time is measured in these units the scaled number of particles converges to a variant of neveu s continuous state branching process furthermore the genealogy of the particles is then governed by a coalescent process known as the bolthausen sznitman coalescent this validates the non rigorous predictions by brunet derrida muller and munier for a closely related model

asymptotic behavior analysis of a coupled time varying system application to adaptive systems asymptotic behavior of a partial state of a coupled ordinary and or partial differential equation is investigated it is specifically shown that if a signal x t is a solution to a dynamic system existing for all t spl ges 0 in an abstract banach space and pth p spl ges 1 power integrable then x t spl rarr 0 as t spl rarr spl infin the system is allowed to be nonautonomous and assumes the existence of a lyapunov function since the derivative of the lyapunov function is negative semidefinite stability or uniform stability in the sense of lyapunov would be concluded however this paper further asserts that the partial state which remains in the time derivative of the lyapunov function converges to zero asymptotically

vibrational stabilization of nonlinear parabolic systems with neumann boundary conditions the conditions for the existence of the stabilizing vibrations for a class of distributed parameter systems governed by parabolic partial differential equations with neumann boundary conditions are derived the guidelines for the choice of the vibration parameters that ensure stabilization are given examples of vibrational stabilization of unstable systems by linear multiplicative and vector additive vibrations are given to support the theory

two representations of a conditioned superprocess we consider a class of measure valued markov processes constructed by taking a superprocess over some underlying markov process and conditioning it to stay alive forever we obtain two representations of such a process the first representation is in terms of an immortal particle that moves around according to the underlying markov process and throws off pieces of mass which then proceed to evolve in the same way that mass evolves for the unconditioned superprocess as a consequence of this representation we show that the tail field of the conditioned superprocess is trivial if the tail field of the underlying process is trivial the second representation is analogous to one obtained by legall in the unconditioned case it represents the conditioned superprocess in terms of a certain process taking values in the path space of the underlying process this representation is useful for studying the transience and recurrence properties of the closed support process

degenerate stochastic differential equations and super markov chains we consider diffusions corresponding to the generator for continuous with i nonnegative we show uniqueness for the corresponding martingale problem under certain non degeneracy conditions on b i i and present a counter example when these conditions are not satisfied as a special case we establish uniqueness in law for some classes of super markov chains with state dependent branching rates and spatial motions

application of averaging method for integro differential equations to model reference adaptive control of parabolic systems abstract an averaging theorem for integro differential equations is applied to the convergence analysis of controller parameters of a model reference adaptive control algorithm for a class of parabolic partial differential equations with constant coefficients the stability of an adaptive control algorithm is proven as well

stationary distributions for a class of generalized fleming viot processes we identify stationary distributions of generalized fleming viot processes with jump mechanisms specified by certain beta laws together with a parameter measure each of these distributions is obtained from normalized stable random measures after a suitable biased transformation followed by mixing by the law of a dirichlet random measure with the same parameter measure the calculations are based primarily on the well known relationship to measure valued branching processes with immigration

adaptive boundary control of a flexible manipulator with input saturation abstractin this study we consider the anti windup design as one of the approaches for the boundary control problem of a flexible manipulator in the presence of system parametric uncertainties external disturbances and bounded inputs the dynamics of the system are represented by partial differential equations pdes using the singular perturbation approach the pde model is divided into two simpler subsystems with the lyapunov s direct method an adaptive boundary control scheme is developed to regulate the angular position and suppress the elastic vibration simultaneously and the adaptive laws are designed to compensate for the system parametric uncertainties and the disturbances the proposed control scheme allows the application of smooth hyperbolic functions which satisfy physical conditions and input restrictions be easily realised numerical simulations demonstrate the effectiveness of the proposed scheme

analysis and design of oscillatory control systems this paper presents analysis and design results for control systems subject to oscillatory inputs i e inputs of large amplitude and high frequency the key analysis results are a series expansion characterizing the averaged system and various lie algebraic conditions that guarantee the series can be summed various example systems provide insight into the results with regards to design we recover and extend a variety of point stabilization and trajectory tracking results using oscillatory controls we present novel developments on stabilization of systems with positive trace and on tracking for second order underactuated systems

vibrational control of nonlinear time lag systems with bounded delay averaging theory stabilizability and transient behavior this paper develops the theory of vibrational control of nonlinear time lag systems with arbitrarily large but bounded delay averaging theory for fast oscillating differential delay equations is presented and then applied to vibrational control conditions are given which ensure the existence of parametric vibrations that stabilize nonlinear time lag systems transient behavior is also discussed illustrative examples are given which show 1 the feasibility of the theory to important applications and 2 the differences in the theory presented and the existing known theory for vibrational control of ordinary differential equations