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

extracting macroscopic stochastic dynamics model problems the purpose of this work is to shed light on an algorithm designed to extract effective macroscopic models from detailed microscopic simulations the particular algorithm we study is a recently developed transfer operator approach due to schutte et al 20 the investigations involve the formulation and subsequent numerical study of a class of model problems the model problems are ordinary differential equations constructed to have the property that when projected onto a low dimensional subspace the dynamics is approximately that of a stochastic differential equation exhibiting a finite state space markov chain structure the numerical studies show that the transfer operator approach can accurately extract finite state markov chain behavior embedded within high dimensional ordinary differential equations in so doing the studies lend considerable weight to existing applications of the algorithm to the complex systems arising in applications such as molecular dynamics the algorithm is predicated on the assumption of markovian input data further numerical studies probe the role of memory effects although preliminary these studies of memory indicate interesting avenues for further development of the transfer operator methodology

extended convergence to continuous in probability processes with independent increments a special extended kind of convergence in distribution of processes with filtration is considered recent theorems on the functional convergence of semimartingales are improved by showing that their assumptions imply the extended convergence of semimartingales to continuous in probability processes with independent increments

follmer schweizer decomposition and mean variance hedging for general claims let x be an r d valued special semimartingale on a probability space f f t 0 t t p with decomposition x x 0 m a and the space of all predictable x integrable processes such that dx is in the space s 2 of semimartingales if h is a random variable in l 2 we prove under additional assumptions on the process x that h can be written as the sum of an f 0 measurable random variable h 0 a stochastic integral of x and a martingale part orthogonal to m moreover this decomposition is unique and the function mapping h with its decomposition is continuous with respect to the l 2 norm finally we deduce from this continuity that the subspace of l 2 generated by dx where is closed in l 2 and we give some applications of this result to financial mathematics

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

variance optimal hedging in discrete time we solve the problem of approximating in 2 a given random variable h by stochastic integrals gt of a given discrete time process x we interpret h as a contingent claim to be paid out at time t x as the price evolution of some risky asset in a financial market and g as the cumulative gains from trade using the hedging strategy as an application we determine the variance optimal strategy which minimizes the variance of the net loss h gt over all strategies

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

stochastic differential equations with reflecting boundary conditions on resout des equations differentielles stochastiques a conditions aux limites reflechissantes par une approche directe basee sur le probleme de skorokhod

on contact anosov flows exponential decay of correlations for co 4 contact anosov flows is established this implies in particular exponential decay of correlations for all smooth geodesic flows in strictly negative curvature

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

stochastic perturbation of sweeping process and a convergence result for an associated numerical scheme abstract here we present well posedness results for first order stochastic differential inclusions more precisely for sweeping process with a stochastic perturbation these results are provided in combining both deterministic sweeping process theory recently developed in edmond and thibault 2005 2006 18 19 and methods concerning the reflection of a brownian motion lions and sznitman 1984 23 and saisho 1987 31 in addition we prove convergence results for an euler scheme discretizing these stochastic differential inclusions

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

a vector valued almost sure invariance principle for hyperbolic dynamical systems we prove an almost sure invariance principle approximation by d dimensional brownian motion for vector valued holder observables of large classes of nonuniformly hyperbolic dynamical systems these systems include axiom a dieomorphisms and flows as well as systems modelled by young towers with moderate tail decay rates in particular the position variable of the planar periodic lorentz gas with finite horizon approximates a 2 dimensional brownian motion

statistical properties for flows with unbounded roof function including the lorenz attractor for geometric lorenz attractors including the classical lorenz attractor we obtain a greatly simplified proof of the central limit theorem which applies also to the more general class of codimension two singular hyperbolic attractors we also obtain the functional central limit theorem and moment estimates as well as iterated versions of these results a consequence is deterministic homogenisation convergence to a stochastic differential equation for fast slow dynamical systems whenever the fast dynamics is singularly hyperbolic of codimension two

estimation of the variances in the branching process with immigration estimation theory for the variances of the offspring and immigration distributions in a simple branching process with immigration is developed analogous to the estimation theory for the means given by wei and winnicki 1990 conditional and weighted conditional least squares estimators are considered and their asymptotic properties for the full range of parameters are studied nonexistence of consistent estimators in the critical case is established which complements analogous result of wei and winnicki for the supercritical case

stability of mixing and rapid mixing for hyperbolic flows we obtain general results on the stability of mixing and rapid mixing superpolynomial decay of correlations for hyperbolic flows amongst c r axiom a flows r 2 we show that there is a c 2 open c r dense set of flows for which each nontrivial hyperbolic basic set is rapid mixing this is the first general result on the stability of rapid mixing or even mixing for axiom a

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

all adapted topologies are equal a number of researchers have introduced topological structures on the set of laws of stochastic processes a unifying goal of these authors is to strengthen the usual weak topology in order to adequately capture the temporal structure of stochastic processes aldous defines an extended weak topology based on the weak convergence of prediction processes in the economic literature hellwig introduced the information topology to study the stability of equilibrium problems bion nadal and talay introduce a version of the wasserstein distance between the laws of diffusion processes pflug and pichler consider the nested distance and the weak nested topology to obtain continuity of stochastic multistage programming problems these distances can be seen as a symmetrization of lassalle s causal transport problem but there are also further natural ways to derive a topology from causal transport our main result is that all of these seemingly independent approaches define the same topology in finite discrete time moreover we show that this weak adapted topology is characterized as the coarsest topology that guarantees continuity of optimal stopping problems for continuous bounded reward functions

conjugate dynamics on center manifolds for stochastic partial differential equations abstract in this paper we prove that for a random differential equation with the driving noise constructed from a q wiener process and the wiener shift there exists a local center unstable stable center unstable center stable manifold and a local stable foliation an unstable foliation on the center unstable manifold and a stable foliation on the center stable manifold the smoothness of which depend on the vector fields of the equation also we show that any two arbitrarily local center manifolds constructed as above are conjugate

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

statistical properties of dynamical systems with some hyperbolicity this paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts though not necessarily all of their phase spaces the main results are for discrete time systems to put this work into context recall that for axiom a attractors the picture has been fairly complete since the 1970 s see s1 b r2 since then much progress has been made on two fronts there is a general nonuniform theory that deals with properties common to all diffeomorphisms with nonzero lyapunov exponents o p1 ka ly and there are detailed analyses of specific kinds of dynamical systems including for example billiards 1 dimensional and henon type maps s2 bsc hk j bc2 by1 statistical properties such as exponential decay of correlations are not enjoyed by all diffeomorphisms with nonzero lyapunov exponents the goal of this paper is a systematic understanding of these and other properties for a class of dynamical systems larger than axiom a this class will not be defined explicitly but it includes some of the much studied examples by looking at regular returns to sets with good hyperbolic properties one could give systems in this class a simple dynamical representation conditions for the existence of natural invariant measures exponential mixing and central limit theorems are given in terms of the return times these conditions can be checked in concrete situations giving a unified way of proving a number of results some new and some old among the new results are the exponential decay of correlations for a class of scattering billiards and for a positive measure set of henon type maps

explicit form and robustness of martingale representations stochastic integral representation of martingales has been undergoing a renaissance due to questions motivated by stochastic finance theory in the brownian case one usually has formulas of differing degrees of exactness for the predictable integrands we extend some of these to markov cases where one does not necessarily have stochastic integral representation of all martingales moreover we study various convergence questions that arise naturally from for example approximations of price processes via euler schemes for solutions of stochastic differential equations we obtain general results of the following type let u u n be random variables with decompositions u alpha int 0 infty xi s dx s n infty u n alpha n int 0 infty xi n s dx n s n n infty where x n x n n n are martingales if x n to x and u n to u when and how does xi n rightarrow xi

large deviations for nonuniformly hyperbolic systems we obtain large deviation estimates for a large class of nonuniformly hyperbolic systems namely those modelled by young towers with summable decay of correlations in the case of exponential decay of correlations we obtain exponential large deviation estimates given by a rate function in the case of polynomial decay of correlations we obtain polynomial large deviation estimates and exhibit examples where these estimates are essentially optimal in contrast with many treatments of large deviations our methods do not rely on thermodynamic formalism hence for holder observables we are able to obtain exponential estimates in situations where the space of equilibrium measures is not known to be a singleton as well as polynomial estimates in situations where there is not a unique equilibrium measure

slow rates of mixing for dynamical systems with hyperbolic structures we consider invertible discrete time dynamical systems having a hyperbolic product structure in some region of the phase space with infinitely many branches and variable return time we show that the decay of correlations of the srb measure associated to that hyperbolic structure is related to the tail of the recurrence times we also give sufficient conditions for the validity of the central limit theorem this extends previous results by young in ann math 147 585 650 1998 israel j math 110 153 188 1999

a non convex setup for multivalued differential equations driven by oblique subgradients abstract the paper proves the existence and uniqueness of the solution for the following multivalued deterministic variational inequality with oblique subgradients considered in a non convex domain x t h t x t x t g t x t t 0 x 0 x 0 where stands for the frechet subdifferential of the semiconvex function and the matrix application x h x is a lipschitz mapping the presence of the oblique reflection brought by the term h leads to the use of different techniques comparing to the cases of standard reflection in non convex domains or oblique reflection in convex domains the last section of the article is focused on the qualitative analysis of a non convex skorohod problem with generalized reflection and as applications stochastic variational inequalities driven by oblique frechet subgradients are addressed

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

superdiffusive limits for deterministic fast slow dynamical systems we consider deterministic fast slow dynamical systems on mathbb r m times y of the form begin aligned left begin array ll x k 1 n x k n n 1 a big x k n big n 1 alpha b big x k n big v y k y k 1 f y k end array right end aligned where alpha in 1 2 under certain assumptions we prove convergence of the m dimensional process x n t x lfloor nt rfloor n to the solution of the stochastic differential equation begin aligned mathrm d x a x mathrm d t b x diamond mathrm d l alpha end aligned where l alpha is an alpha stable levy process and diamond indicates that the stochastic integral is in the marcus sense in addition we show that our assumptions are satisfied for intermittent maps f of pomeau manneville type

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

reversible systems with first integrals abstract a reversible system of ordinary differential equations ode possessing some first integrals is considered a simple description of the first integral space is given it is shown that under the auxiliary assumption that the integrals are symmetric i e they do not change sign under the action of the reversing involution the presence of the integrals allows one to bring the problem of dynamical stability for a symmetric equilibrium to the similar problem but for the reduced system the reduced system is merely the restriction of the initial system to the intersection of the surfaces of level of the integrals passing through the equilibrium

sweeping by a continuous prox regular set abstract the evolution problem known as sweeping process is considered for a class of nonconvex sets called prox regular or convex assuming essentially that such sets contain in the interior a suitable subset and move continuously w r t the hausdorff distance we prove local and global existence as well as uniqueness of solutions which are continuous functions with bounded variation some examples are presented

a spectral approach for quenched limit theorems for random expanding dynamical systems we prove quenched versions of i a large deviations principle ldp ii a central limit theorem clt and iii a local central limit theorem lclt for non autonomous dynamical systems a key advance is the extension of the spectral method commonly used in limit laws for deterministic maps to the general random setting we achieve this via multiplicative ergodic theory and the development of a general framework to control the regularity of lyapunov exponents of twisted transfer operator cocycles with respect to a twist parameter while some versions of the ldp and clt have previously been proved with other techniques the local central limit theorem is to our knowledge a completely new result and one that demonstrates the strength of our method applications include non autonomous piecewise expanding maps defined by random compositions of the form t n 1 t t an important aspect of our results is that we only assume ergodicity and invertibility of the random driving in particular no expansivity or mixing properties are required

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

majorization doubly stochastic matrices and comparison of eigenvalues abstract 1 basic properties of majorization 2 isotone maps and algebraic operations 3 double sub and superstochasticity 4 doubly stochastic matrices 5 doubly stochastic matrices with minimum permanent 6 comparison of eigenvalues 7 doubly stochastic maps

superadditivity and derivative of operator functions abstract we will show that if i j a i a j 0 for bounded operators a i 0 i 1 2 n then g i a i i g a i for every operator convex function g t on 0 with g 0 0 in particular i a i log i a i i a i log a i if each a i is invertible let a b 0 and a be invertible then we will observe that the frechet derivative d g s a b is increasing on 0 s for every operator convex function g t on 0 if and only if a b b a 0

almost sure invariance principle for nonuniformly hyperbolic systems we prove an almost sure invariance principle that is valid for general classes of nonuniformly expanding and nonuniformly hyperbolic dynamical systems discrete time systems and flows are covered by this result in particular the result applies to the planar periodic lorentz flow with finite horizon statistical limit laws such as the central limit theorem the law of the iterated logarithm and their functional versions are immediate consequences

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

probleme de skorohod multivoque on prouve un resultat d existence et d unicite pour une generalisation par introduction d un operateur maximal monotone multivoque du probleme de skorohod avec reflexion normale deterministe associe a un convexe ferme d de r d la formulation a partir des operateurs maximaux monotones multivoques permet de considerer des drifts singuliers explosant au bord du domaine cette approche multivoque clarifie la connexion entre probleme de skorohod et semigroupes nonlineaires en guise d application on considere ensuite le cas stochastique les equations differentielles stochastiques multivoques sont ainsi revisitees par consequent cette contribution fournit une nouvelle methode de construction de diffusions reflechies normalement possedant un coefficient de derive discontinu explosif

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

almost sure invariance principle for dynamical systems by spectral methods we prove the almost sure invariance principle for stationary d valued random processes with very precise dimension independent error terms solely under a strong assumption concerning the characteristic functions of these processes this assumption is easy to check for large classes of dynamical systems or markov chains using strong or weak spectral perturbation arguments

monotone stability of quadratic semimartingales with applications to unbounded general quadratic bsdes in this paper we study the stability and convergence of some general quadratic semimartingales motivated by financial applications we study simultaneously the semimartingale and its opposite their characterization and integrability properties are obtained through some useful exponential submartingale inequalities then a general stability result including the strong convergence of the martingale parts in various spaces ranging from h1 to bmo is derived under some mild integrability condition on the exponential of the terminal value of the semimartingale this can be applied in particular to bsde like semimartingales this strong convergence result is then used to prove the existence of solutions of general quadratic bsdes under minimal exponential integrability assumptions relying on a regularization in both linear quadratic growth of the quadratic coefficient itself on the contrary to most of the existing literature it does not involve the seminal result of kobylanski ann probab 28 2010 558 602 on bounded solutions

linearizability conditions of a time reversible quartic like system in this paper we study the linearizability problem of polynomial like complex differential systems we give a reduction of linearizability problem of such non polynomial systems to the problem of polynomial systems applying this reduction we find some linearizability conditions for a time reversible quartic like complex system and derive from them conditions of isochronous center for the corresponding real system

limit theorems for partially hyperbolic systems we consider a large class of partially hyperbolic systems containing among others affine maps frame flows on negatively curved manifolds and mostly contracting diffeomorphisms if the rate of mixing is sufficiently high the system satisfies many classical limit theorems of probability theory

bv solutions of nonconvex sweeping process differential inclusion with perturbation abstract this paper is devoted to the study of differential inclusions particularly discontinuous perturbed sweeping processes in the infinite dimensional setting on the one hand the sets involved are assumed to be prox regular and to have a variation given by a function which is of bounded variation and right continuous on the other hand the perturbation satisfies a linear growth condition with respect to a fixed compact subset finally the case where the sets move in an absolutely continuous way is recovered as a consequence

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

rapid decay of correlations for nonuniformly hyperbolic flows we show that superpolynomial decay of correlations rapid mixing is prevalent for a class of nonuniformly hyperbolic flows these flows are the continuous time analogue of the class of nonuniformly hyperbolic maps for which young proved exponential decay of correlations the proof combines techniques of dolgopyat and operator renewal theory it follows from our results that planar periodic lorentz flows with finite horizons and flows near homoclinic tangencies are typically rapid mixing

effective stability for a hamiltonian system near an elliptic equilibrium point with an application to the restricted three body problem abstract we consider an n degrees of freedom hamiltonian system near an elliptic equilibrium point the system is put in normal form up to an arbitrary order and with respect to some resonance module and estimates are obtained for both the size of the remainder and for the domain of convergence of the transformation leading to normal form a bound to the rate of diffusion is thus found and by optimizing the order of normalization exponential estimates of nekhoroshev s type are obtained this provides explicit estimates for the stability properties of the elliptic point and leads in some cases to effective stability i e stability up to finite but long times an application to the stability of the triangular libration points in the spatial restricted three body is also given

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

inference for stochastic neuronal models stochastic models of some aspects of the electrical activity in the nervous system at the cellular level are developed in particular models of the subthreshold behavior of the membrane potential of neurons are considered along with the problem of estimation of physiologically meaningful parameters of the developed models both ordinary and partial stochastic differential equation models are treated

time reversal symmetry in dynamical systems a survey abstract in this paper we survey the topic of time reversal symmetry in dynamical systems we begin with a brief discussion of the position of time reversal symmetry in physics after defining time reversal symmetry as it applies to dynamical systems we then introduce a major theme of our survey namely the relation of time reversible dynamical sytems to equivariant and hamiltonian dynamical systems we follow with a survey of the state of the art on the theory of reversible dynamical systems including results on symmetric periodic orbits local bifurcation theory homoclinic orbits and renormalization and scaling some areas of physics and mathematics in which reversible dynamical systems arise are discussed in an appendix we provide an extensive bibliography on the topic of time reversal symmetry in dynamical systems

existence of solutions to the nonconvex sweeping process abstract in this note we prove the existence of solutions for the sweeping process problem x t nc t x t a e x t c t x 0 x0 c 0 where c is an arbitrary hausdorff lipschitzean multifunction from i 0 t onto the set of nonempty closed subsets of r d this generalizes a well known result of j j moreau 1971 in sem d analyse convexe montpelier exp 15 in the convex case

sweeping process with regular and nonregular sets abstract differential inclusions involving the normal cone to a moving set are investigated a special attention is paid to the sweeping process associated with sets for which no regularity assumption is required

convergence in distribution and skorokhod convergence for the general theory of processes this paper proves some skorokhod convergence theorems for processes with filtration roughly these are theorems which say that if a family of processes with filtration x n n n converges in distribution in a suitable sense then there exists a family of equivalent processes y n n n which converges almost surely the notion of equivalence used is that of adapted distribution which guarantees that each x n n has the same stochastic properties as x n n with respect to its filtration such as the martingale property or the markov property the appropriate notion of convergence in distribution is convergence in adapted distribution which is developed in the paper fortunately any tight sequence of processes has a subsequence which converges in adapted distribution for discrete time processes y n n n and their limit y may be taken as all having the same fixed filtration n in the continuous time case they n n may require different filtrations n which converge to to handle this convergence of filtrations is defined and its theory developed