boundedness and convergence of some self attracting diffusions we consider some self attracting diffusions and study the behaviour of their paths when time tends to infinity we prove that in case the interaction is nonlocal the paths are bounded a s even if they don t converge otherwise we generalize the convergence result of m cranston and y le jan

strong convergence rates for cox ingersoll ross processes full parameter range abstract we study strong pathwise approximation of cox ingersoll ross processes we propose a milstein type scheme that is suitably truncated close to zero where the diffusion coefficient fails to be locally lipschitz continuous for this scheme we prove positive convergence rates for the full parameter range including the accessible boundary regime the error criterion is given by the maximal l p distance of the solution and its approximation on a compact interval in the particular case of a squared bessel process of dimension 0 the convergence rate is given by min 1 2 p

simulation of stopped diffusions in this work we study standard euler updates for simulating stopped diffusions as an immediate application we discuss the computation of first exit times of diffusions from a domain we focus on one dimensional situations and show how the ideas for the simulation of killed diffusions can be adapted to this problem in particular we give a fully implementable algorithm to compute the first exit time from an interval numerically the brownian motion case is treated in detail and extensions to general diffusions are given special emphasis is given to numerical experiments for every ansatz we include numerical experiments confirming the conjectured accuracy of our methods our algorithm is of order one in a weak sense comparisons with other algorithms are shown results that are superior to those obtained with other methods are presented when approximating a first hitting time distribution the results obtained with our algorithm are much better than those achieved with other methods

bilinear mixed effects models for dyadic data this article discusses the use of a symmetric multiplicative interaction effect to capture certain types of third order dependence patterns often present in social networks and other dyadic datasets such an effect along with standard linear fixed and random effects is incorporated into a generalized linear model and a markov chain monte carlo algorithm is provided for bayesian estimation and inference in an example analysis of international relations data accounting for such patterns improves model fit and predictive performance

where do brownian particles spend their time abstract we study statistical properties of the fraction of time spent by a brownian particle in different regions of space also treated in our analysis are the effects of one or more constraints on the trajectory at different times we show that the effects of imposing n constraints can be analyzed in terms of the probability density of the residence time for a single constraint an analogy to the description of the spatial density of a polymer chain is proposed and applied to evaluate the monomeric density in some specific examples

quenched asymptotics of the ground state energy of random schrodinger operators with scaled gibbsian potentials this article describes the almost sure infinite volume asymptotics of the ground state energy of random schrodinger operators with scaled gibbsian potentials the random potential is obtained by distributing soft obstacles according to an infinite volume grand canonical tempered gibbs measure with a superstable pair interaction there is no restriction on the strength of the pair interaction it may be taken e g at a critical point the potential is scaled with the box size in a critical way i e the scale is determined by the typical size of large deviations in the gibbsian cloud the almost sure infinite volume asymptotics of the ground state energy is described in terms of two equivalent deterministic variational principles involving only thermodynamic quantities the qualitative behaviour of the ground state energy asymptotics is analysed depending on the dimension and on the holder exponents of the free energy density it is identified which cases lead to a phase transition of the asymptotic behaviour of the ground state energy

sobolev differentiable stochastic flows for sdes with singular coefficients applications to the transport equation in this paper we establish the existence of a stochastic flow of sobolev diffeomorphisms r d x 7 s t x r d s t r for a stochastic differential equation sde of the form dxt b t xt dt dbt s t r xs x r d the above sde is driven by a bounded measurable drift coefficientb r r d r d and a d dimensional brownian motion b more specifically we show that the stochastic flow s t of the sde lives in the space l 2 w 1 p r d w for all s t and all p 1 where w 1 p r d w denotes a weighted sobolev space with weight w possessing a p th moment with respect to lebesgue measure on r d this result is counter intuitive since the dominant culture in stochastic and deterministic dynamical systems is that the flow inherits its spatial regularity from the driving vector fields the spatial regularity of the stochastic flow yields existence and uniqueness of a sobolev differentiable weak solution of the stratonovich stochastic transport equation dtu t x b t x du t x dt p d 1 ei du t x db i t 0 u 0 x u0 x where b is bounded and measurable u0 is c 1 b and ei d 1 a basis for r d it is well known that the deterministic counter part of the above equation does not in general have a solution using stochastic perturbations and our analysis of the above sde we establish a deterministic flow of sobolev diffeomorphisms for classical one dimensional deterministic ode s driven by discontinuous vector fields furthermore and as a corollary of the latter result we construct a sobolev stochastic flow of diffeomorphisms for one dimensional sde s driven by discontinuous diffusion coefficients

pressure stability in fractional step finite element methods for incompressible flows abstract the objective of this paper is to analyze the pressure stability of fractional step finite element methods for incompressible flows that use a pressure poisson equation for the classical first order projection method it is shown that there is a pressure control which depends on the time step size and therefore there is a lower bound for this time step for stability reasons the situation is much worse for a second order scheme in which part of the pressure gradient is kept in the momentum equation the pressure stability in this case is extremely weak to overcome these shortcomings a stabilized fractional step finite element method is also considered and its stability is analyzed some simple numerical examples are presented to support the theoretical results

brownian intersection local times exponential moments and law of large masses consider p independent brownian motions in r d each running up to its first exit time from an open domain b and their intersection local time las a measure on b we give a sharp criterion for the finiteness of exponential moments e exp n i 1 1 p where 1 n are nonnegative bounded functions with compact support in b we also derive a law of large numbers for intersection local time conditioned to have large total mass

optimal stopping of linear diffusions with random discounting we propose a new solution method for optimal stopping problems with random discounting for linear diffusions whose state space has a combination of natural absorbing or reflecting boundaries the method uses a concave characterization of excessive functions for linear diffusions killed at a rate determined by a markov additive functional and reduces the original problem to an undiscounted optimal stopping problem for a standard brownian motion the latter can be solved essentially by inspection the necessary and sufficient conditions for the existence of an optimal stopping rule are proved when the reward function is continuous the results are illustrated on examples

brownian survival among poissonian traps with random shapes at critical intensity in this paper we consider a standard brownian motion in d starting at 0 and observed until time t the brownian motion takes place in the presence of a poisson random field of traps whose centers have intensity t and whose shapes are drawn randomly and independently according to a probability distribution on the set of closed subsets of d subject to appropriate conditions the brownian motion is killed as soon as it hits one of the traps with the help of a large deviation technique developed in an earlier paper we find the tail of the probability s t that the brownian motion survives up to time t when

latent space approaches to social network analysis network models are widely used to represent relational information among interacting units in studies of social networks recent emphasis has been placed on random graph models where the nodes usually represent individual social actors and the edges represent the presence of a specified relation between actors we develop a class of models where the probability of a relation between actors depends on the positions of individuals in an unobserved social space we make inference for the social space within maximum likelihood and bayesian frameworks and propose markov chain monte carlo procedures for making inference on latent positions and the effects of observed covariates we present analyses of three standard datasets from the social networks literature and compare the method to an alternative stochastic blockmodeling approach in addition to improving on model fit for these datasets our method provides a visual and interpretable model based spatial representation of social relationships and improv

evolution implementation and application of level set and fast marching methods for advancing fronts abstract a variety of numerical techniques are available for tracking moving interfaces in this review we concentrate on techniques that result from the link between the partial differential equations that describe moving interfaces and numerical schemes designed for approximating the solutions to hyperbolic conservation laws this link gives rise to computational techniques for tracking moving interfaces in two and three space dimensions under complex speed laws we discuss the evolution of these techniques the fundamental numerical approximations involved implementation details and applications in particular we review some work on three aspects of materials sciences semiconductor process simulations seismic processing and optimal structural topology design

variational formulations for surface tension capillarity and wetting the interest in the simulation of flows with significant surface tension effects has grown significantly in recent years this has been driven by the substantial advances made in the measurement and manufacturing of microscopic systems since at small length scales surface phenomena are dominant in this article surface tension capillarity and wetting effects are discussed in terms of the virtual work principle and shape sensitivity starting from first principles and arriving at variational formulations that are adequate for numerical treatment by finite elements for example to make the exposition self contained some elements of differential geometry are recalled using a formulation that is fully in cartesian coordinates and may thus be more friendly to readers not familiar with covariant derivatives all necessary results are proved in this cartesian formulation several numerical examples computed with a finite element level set formulation are used to illustrate this challenging physical problem

estimating quadratic variation when quoted prices change by a constant increment abstract for financial assets whose best quotes almost always change by jumping by the market s price tick size one cent five cents etc this paper proposes an estimator of quadratic variation which controls for microstructure effects it measures the prevalence of alternations where quotes jump back to their just previous price it defines a simple property called uncorrelated alternation which under conditions implies that the estimator is consistent in an asymptotic limit theory where jumps become very frequent and small feasible limit theory is developed and in simulations works well

a projection fem for variable density incompressible flows abstract this work describes a new finite element projection method for the computation of incompressible viscous flows of nonuniform density one original idea of the proposed method consists in factorizing the density variable partly outside and partly inside the time evolution operator in the momentum equation to prevent spatial discretization errors in the mass conservation to affect the kinetic energy balance of the fluid it is shown that unconditional stability in the incremental version of the projection method is possible provided two projections are performed per time step in particular a second order accurate bdf projection method is presented and its numerical performance is illustrated by test computations and comparisons

optimal switching for the pairs trading rule a viscosity solutions approach abstract this paper studies the problem of determining the optimal cut off for pairs trading rules we consider two cointegrated assets whose spread is modelled by a general mean reverting process and the optimal pair trading rule is formulated as an optimal switching problem between three regimes flat position no holding stocks one long and the other short and one short and the other long a fixed commission cost is charged with each transaction we use a viscosity solutions approach to prove the existence and the explicit characterisation of cut off points via the resolution of quasi algebraic equations we illustrate our results by numerical simulations

handbook of brownian motion facts and formulae i theory i stochastic processes in general ii linear diffusions iii stochastic calculus iv brownian motion v local time as a markov process vi differential systems associated to brownian motion appendix 1 briefly on some diffusions ii tables of distributions of functionals of brownian motion and related processes 1 brownian motion 2 brownian motion with drift 3 reflecting brownian motion 4 bessel process of order 5 bessel process of order 1 2 6 bessel process of order zero 7 ornstein uhlenbeck process 8 radial ornstein uhlenbeck process 9 geometric brownian motion appendix 2 special functions appendix 3 inverse laplace transforms appendix 4 differential equations and their solutions appendix 5 formulae for n fold differentiation

a stabilized finite point method for analysis of fluid mechanics problems in this paper a meshless procedure termed the finite point method for solving convection diffusion and fluid flow type problems is presented the method is based on the use of a weighted least square interpolation procedure together with point collocation for evaluating the approximation integrals special emphasis is given to the stabilization of the convective terms and the neumann boundary condition which has been found to be essential to obtain accurate results some examples of application to diffusive and convective transport and compressible flow problems using quadratic fp interpolations are presented

lagrangian versus eulerian integration errors abstract the possibility to use a lagrangian frame to solve problems with large time steps was successfully explored previously by the authors for the solution of homogeneous incompressible fluids and also for solving multi fluid problems idelsohn et al 2012 2014 2013 the strategy used by the authors was named particle finite element method second generation pfem 2 the objective of this paper is to demonstrate in which circumstances the use of a lagrangian frame with particles is more accurate than a classical eulerian finite element method and when large time steps and or coarse meshes may be used

assessing a mixture model for clustering with the integrated completed likelihood we propose an assessing method of mixture model in a cluster analysis setting with integrated completed likelihood for this purpose the observed data are assigned to unknown clusters using a maximum a posteriori operator then the integrated completed likelihood icl is approximated using the bayesian information criterion bic numerical experiments on simulated and real data of the resulting icl criterion show that it performs well both for choosing a mixture model and a relevant number of clusters in particular icl appears to be more robust than bic to violation of some of the mixture model assumptions and it can select a number of dusters leading to a sensible partitioning of the data

span observables when is a foraging rabbit no longer hungry be x t a random walk we study its span s i e the size of the domain visited up to time t we want to know the probability that s reaches 1 for the first time as well as the density of the span given t analytical results are presented and checked against numerical simulations we then generalize this to include drift and one or two reflecting boundaries we also derive the joint probability of the maximum and minimum of a process our results are based on the diffusion propagator with reflecting or absorbing boundaries for which a set of useful formulas is derived

estimation and prediction for stochastic blockstructures a statistical approach to a posteriori blockmodeling for digraphs and valued digraphs is proposed the probability model assumes that the vertices of the digraph are partitioned into several unobserved latent classes and that the probability distribution of the relation between two vertices depends only on the classes to which they belong a bayesian estimator based on gibbs sampling is proposed the basic model is not identified because class labels are arbitrary the resulting identifiability problems are solved by restricting inference to the posterior distributions of invariant functions of the parameters and the vertex class membership in addition models are considered where class labels are identified by prior distributions for the class membership of some of the vertices the model is illustrated by an example from the social networks literature kapferer s tailor shop

large deviations for brownian motion in a random scenery we prove large deviations principles in large time for the brownian occupation time in random scenery frac 1 t int 0 t xi b s ds the random field is constant on the elements of a partition of d into unit cubes these random constants say left lbrace xi j j in mathbb z d right rbrace consist of i i d bounded variables independent of the brownian motion bs s 0 this model is a time continuous version of kesten and spitzer s random walk in random scenery we prove large deviations principles in quenched and annealed settings

skew cir process conditional characteristic function moments and bond pricing abstract this paper is concerned with one general feller s branching diffusion called skew cir process we derive the conditional characteristic function and moment of this general diffusion process first then with the same computing idea we handle with its application in bond pricing all the results we adopt are closed forms

growth of the brownian forest trees in brownian excursions have been studied since the late 1980s forests in excursions of brownian motion above its past minimum are a natural extension of this notion in this paper we study a forest valued markov process which describes the growth of the brownian forest the key result is a composition rule for binary galton watson forests with i i d exponential branch lengths we give elementary proofs of this composition rule and explain how it is intimately linked with williams decomposition for brownian motion with drift

derivation of stabilized equations for numerical solution of advective diffusive transport and fluid flow problems abstract the concept of the so called artificial or balancing diffusion used to stabilize the numerical solution of advective diffusive transport and fluid flow problems is revised in this paper it is shown that the standard forms of the balancing diffusion terms usually chosen in a heuristic manner can be naturally found by introducing higher order approximations in the derivation of the governing differential equations via standard conservation or equilibrium principles this allows us to reinterpret many stabilization algorithms and concepts used in every day practice by numerical analysts and also provides an expression for computing the stabilization parameter

analytic solutions for optimal statistical arbitrage trading abstract in this paper we derive analytic formulae for statistical arbitrage trading where the security price follows an ornstein uhlenbeck process by framing the problem in terms of the first passage time of the process we derive expressions for the mean and variance of the trade length and the return we examine the problem of choosing an optimal strategy under two different objective functions the expected return and the sharpe ratio an exact analytic solution is obtained for the case of maximising the expected return

phase transition of the principal dirichlet eigenvalue in a scaled poissonian potential we consider d dimensional brownian motion in a scaled poissonian potential and the principal dirichlet eigenvalue ground state energy of the corresponding schrodinger operator the scaling is chosen to be of critical order i e it is determined by the typical size of large holes in the poissonian cloud we prove existence of a phase transition in dimensions d 4 there exists a critical scaling constant for the potential below this constant the scaled infinite volume limit of the corresponding principal dirichlet eigenvalue is linear in the scale on the other hand for large values of the scaling constant this limit is strictly smaller than the linear bound for d 4 we prove that this phase transition does not take place on that scale further we show that the analogous picture holds true for the partition sum of the underlying motion process

slowdown for time inhomogeneous branching brownian motion we consider the maximal displacement of one dimensional branching brownian motion with macroscopically time varying profiles for monotone decreasing variances we show that the correction from linear displacement is not logarithmic but rather proportional to t 1 3 we conjecture that this is the worse case correction possible

exact simulation of the sabr model the stochastic alpha beta rho sabr model becomes popular in the financial industry because it is capable of providing good fits to various types of implied volatility curves observed in the marketplace however no analytical solution to the sabr model exists that can be simulated directly this paper explores the possibility of exact simulation for the sabr model our contribution is threefold i we propose an exact simulation method for the forward price and its volatility in two special but practically interesting cases i e when the elasticity 1 or when 1 and the price and volatility processes are instantaneously uncorrelated primary difficulties involved are how to simulate two random variables whose distributions can be expressed in terms of the hartman watson and the noncentral chi squared distribution functions respectively two novel simulation schemes are proposed to achieve numerical accuracy efficiency and stability one stems from numerical laplace inversion and asian option literature and the other is based on recent developments in evaluating the noncentral chi squared distribution functions in a robust way numerical examples demonstrate that our method is fast and accurate under various market environments ii when 1 but the price and volatility processes are correlated our simulation method becomes a semi exact one numerical results suggest that it is still quite accurate when the time horizon is not long e g no greater than one year for long time horizons a piecewise semi exact simulation scheme is developed that reduces the biases substantially iii for european option pricing under the sabr model we propose a conditional simulation method which reduces the variance of the plain simulation significantly e g by more than 99 the e companion is available at https doi org 10 1287 opre 2017 1617

a generalization of takane s algorithm for dedicom an algorithm is described for fitting the dedicom model for the analysis of asymmetric data matrices this algorithm generalizes an algorithm suggested by takane in that it uses a damping parameter in the iterative process takane s algorithm does not always converge monotonically based on the generalized algorithm a modification of takane s algorithm is suggested such that this modified algorithm converges monotonically it is suggested to choose as starting configurations for the algorithm those configurations that yield closed form solutions in some special cases finally a sufficient condition is described for monotonic convergence of takane s original algorithm

nonstationary discrete choice this paper develops an asymptotic theory for time series discrete choice models with explanatory variables generated as integrated processes and with multiple choices and threshold parameters determining the choices the theory extends recent work by park and phillips 2000 on binary choice models as in this earlier work the maximum likelihood ml estimator is consistent and has a limit theory with multiple rates of convergence n 3 4 and n 1 4 and mixture normal distributions where the mixing variates depend on brownian local time as well as brownian motion an extended arc sine limit law is given for the sample proportions of the various choices the new limit law exhibits a wider range of potential behavior that depends on the values taken by the threshold parameters

fluid structure interaction using the particle finite element method abstract in the present work a new approach to solve fluid structure interaction problems is described both the equations of motion for fluids and for solids have been approximated using a material lagrangian formulation to approximate the partial differential equations representing the fluid motion the shape functions introduced by the meshless finite element method mfem have been used thus the continuum is discretized into particles that move under body forces gravity and surface forces due to the interaction with neighboring particles all the physical properties such as density viscosity conductivity etc as well as the variables that define the temporal state such as velocity and position and also other variables like temperature are assigned to the particles and are transported with the particle motion the so called particle finite element method pfem provides a very advantageous and efficient way for solving contact and free surface problems highly simplifying the treatment of fluid structure interactions

efficient numerical solution of stochastic differential equations using exponential timestepping we present an exact timestepping method for brownian motion that does not require gaussian random variables to be generated time is incremented in steps that are exponentially distributed random variables boundaries can be explicitly accounted for at each timestep the method is illustrated by numerical solution of a system of diffusing particles

a moving lagrangian interface technique for flow computations over fixed meshes abstract in this paper an enhanced finite element formulation for unsteady incompressible flows with moving interfaces is presented the weak form of the navier stokes equations written using a generalized streamline operator technique is coupled with the movement of the interface between two immiscible fluids defined through an independent moving mesh the position of the interface is updated using a lagrangian formulation in this framework a global mass conservation corrector algorithm and an enhanced element integration technique are proposed to improve accuracy the method is applied to a number of test problems with moving interfaces

symmetry of matrix valued stochastic processes and noncolliding diffusion particle systems as an extension of the theory of dyson s brownian motion models for the standard gaussian random matrix ensembles we report a systematic study of hermitian matrix valued processes and their eigenvalue processes associated with the chiral and nonstandard random matrix ensembles in addition to the noncolliding brownian motions we introduce a one parameter family of temporally homogeneous noncolliding systems of the bessel processes and a two parameter family of temporally inhomogeneous noncolliding systems of yor s generalized meanders and show that all of the ten classes of eigenvalue statistics in the altland zirnbauer classification are realized as particle distributions in the special cases of these diffusion particle systems as a corollary of each equivalence in distribution of a temporally inhomogeneous eigenvalue process and a noncolliding diffusion process a stochastic calculus proof of a version of the harish chandra itzykson zuber formula of integral over unitary group is established

multi fluid flows with the particle finite element method abstract particle methods are those in which the problem is represented by a discrete number of particles each particle moves accordingly with its own mass and the external internal forces applied on it in this paper the particle finite element method based on finite element shape functions is used to solve the continuous fluid mechanics equations in the case of heterogeneous density to evaluate the external applied forces to each particle the incompressible navier stokes equations are solved at each time step using a lagrangian formulation all the information in the fluid is transmitted via the particles all kinds of density heterogeneous fluids and multiphase flows with internal interfaces including or not free surfaces breaking waves and fluid separations may be easily solved with this methodology

two bessel bridges conditioned never to collide double dirichlet series and jacobi theta function it is known that the moments of the maximum value of a one dimensional conditional brownian motion the three dimensional bessel bridge with duration 1 started from the origin are expressed using the riemann zeta function we consider a system of two bessel bridges in which noncolliding condition is imposed we show that the moments of the maximum value is then expressed using the double dirichlet series or using the integrals of products of the jacobi theta functions and its derivatives since the present system will be provided as a diffusion scaling limit of a version of vicious walker model the ensemble of 2 watermelons with a wall the dominant terms in long time asymptotics of moments of height of 2 watermelons are completely determined for the height of 2 watermelons with a wall the average value was recently studied by fulmek by a method of enumerative combinatorics

multidimensional exponential timestepping with boundary test exponential timestepping algorithms are efficient for exit time problems because a boundary test can be performed at the end of each timestep giving high order convergence in numerical evaluation of mean exit times successive time increments are independent random variables with an exponential distribution we show how to perform exact timestepping for brownian motion in more than one dimension and consider hitting times of curved surfaces taking as examples the exit times from a circle from a ball from an ellipse and from the region bounded by the two lines of a hyperbola we report the results of numerical experiments performed with the algorithms developed in this work

gerber shiu analysis in a perturbed risk model with dependence between claim sizes and interclaim times in this paper we consider a compound poisson risk model perturbed by a brownian motion we construct the bivariate cumulative distribution function of the claim size and interclaim time by farlie gumbel morgenstern copula the integro differential equations and the laplace transforms for the gerber shiu functions are obtained we also show that the gerber shiu functions satisfy some defective renewal equations for exponential claims some explicit expressions are obtained and numerical examples for the ruin probabilities are also given

a finite point method in computational mechanics applications to convective transport and fluid flow the paper presents a fully meshless procedure fo solving partial differential equations the approach termed generically the finite point method is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals some examples showing the accuracy of the method for solution of adjoint and non self adjoint equations typical of convective diffusive transport and also to the analysis of compressible fluid mechanics problem are presented

level set methods an overview and some recent results the level set method was devised by s osher and j a sethian 1988 j comput phys 79 12 49 as a simple and versatile method for computing and analyzing the motion of an interface in two or three dimensions bounds a possibly multiply connected region the goal is to compute and analyze the subsequent motion of under a velocity field v this velocity can depend on position time the geometry of the interface and the external physics the interface is captured for later time as the zero level set of a smooth at least lipschitz continuous function x t i e t x x t 0 is positive inside negative outside and is zero on t topological merging and breaking are well defined and easily performed in this review article we discuss recent variants and extensions including the motion of curves in three dimensions the dynamic surface extension method fast methods for steady state problems diffusion generated motion and the variational level set approach we also give a user s guide to the level set dictionary and technology and couple the method to a wide variety of problems involving external physics such as compressible and incompressible possibly reacting flow stefan problems kinetic crystal growth epitaxial growth of thin films vortex dominated flows and extensions to multiphase motion we conclude with a discussion of applications to computer vision and image processing

extremal theory for spectrum of random discrete schrodinger operator i asymptotic expansion formulas we consider the spectral problem for the random schrodinger operator on the multidimensional lattice torus increasing to the whole of lattice with an i i d potential anderson hamiltonian we obtain the explicit almost sure asymptotic expansion formulas for the extreme eigenvalues and eigenfunctions in the intermediate rank case provided the upper distributional tails of potential decay at infinity slower than the double exponential function for the fractional exponential tails including weibull s and gaussian distributions extremal type limit theorems for eigenvalues are proved and the strong influence of parameters of the model on a specification of normalizing constants is described in the proof we use the finite rank perturbation arguments based on the cluster expansion for resolvents

finite calculus formulations for finite element analysis of incompressible flows eulerian ale and lagrangian approaches we present a general formulation for incompressible fluid flow analysis using the finite element method fem the standard eulerian formulation is described first the necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the finite calculus fic method a simple extension of the fluid flow equations to an arbitrary lagrangian eulerian ale frame adequate for treating fluid structure interaction problems is briefly presented a fully lagrangian formulation called the particle finite element method pfem is also described the pfem is particularly attractive for fluid structure interaction problems involving large motions of the free surface and breaking waves examples of application of the eulerian the ale and the fully lagrangian pfem formulations are presented

comparing latent structures of the grade of membership rasch and latent class models this paper focuses on model interpretation issues and employs a geometric approach to compare the potential value of using the grade of membership gom model in representing population heterogeneity we consider population heterogeneity manifolds generated by letting subject specific parameters vary over their natural range while keeping other population parameters fixed in the marginal space based on marginal probabilities and in the full parameter space based on cell probabilities the case of a 2 2 contingency table is discussed in detail and a generalization to 2j tables with j 3 is sketched our approach highlights the main distinction between the gom model and the probabilistic mixture of classes by demonstrating geometrically the difference between the concepts of partial and probabilistic memberships by using the geometric approach we show that in special cases the gom model can be thought of as being similar to an item response theory irt model in representing population heterogeneity finally we show that the gom item parameters can provide quantities analogous to more general logistic irt item parameters as a latent structure model the gom model might be considered a useful alternative for a data analysis when both classes of extreme responses and additional heterogeneity that cannot be captured by those latent classes are expected in the population

on the heat equation with a time dependent singular potential abstract we introduce various classes of potentials on 0 t r n and study the corresponding nonautonomous heat equation given by u t 1 2 u v t x u we prove the existence of the feynman kac propagators for the nonautonomous heat equation and the l p l q smoothing theorem for the propagators

the particle finite element method a powerful tool to solve incompressible flows with free surfaces and breaking waves summary particle methods are those in which the problem is represented by a discrete number of particles each particle moves accordingly with its own mass and the external internal forces applied to it particle methods may be used for both discrete and continuous problems in this paper a particle method is used to solve the continuous fluid mechanics equations to evaluate the external applied forces on each particle the incompressible navier stokes equations using a lagrangian formulation are solved at each time step the interpolation functions are those used in the meshless finite element method and the time integration is introduced by an implicit fractional step method in this manner classical stabilization terms used in the momentum equations are unnecessary due to lack of convective terms in the lagrangian formulation once the forces are evaluated the particles move independently of the mesh all the information is transmitted by the particles fluid structure interaction problems including free fluid surfaces breaking waves and fluid particle separation may be easily solved with this methodology copyright 2004 john wiley sons ltd

model for heterogeneous random networks using continuous latent variables and an application to a tree fungus network the mixture model is a method of choice for modeling heterogeneous random graphs because it contains most of the known structures of heterogeneity hubs hierarchical structures or community structure one of the weaknesses of mixture models on random graphs is that at the present time there is no computationally feasible estimation method that is completely satisfying from a theoretical point of view moreover mixture models assume that each vertex pertains to one group so there is no place for vertices being at intermediate positions the model proposed in this article is a grade of membership model for heterogeneous random graphs which assumes that each vertex is a mixture of extremal hypothetical vertices the connectivity properties of each vertex are deduced from those of the extreme vertices in this new model the vector of weights of each vertex are fixed continuous parameters a model with a vector of parameters for each vertex is tractable because the number of observations is proportional to the square of the number of vertices of the network the estimation of the parameters is given by the maximum likelihood procedure the model is used to elucidate some of the processes shaping the heterogeneous structure of a well resolved network of host parasite interactions

a partitioned fully explicit lagrangian finite element method for highly nonlinear fluid structure interaction problems summary in this work a fully explicit partitioned method for the simulation of fluid structure interaction fsi problems is presented the fluid domain is modelled with an explicit particle finite element method pfem based on the hypothesis of weak compressibility the lagrangian description of the fluid is particularly effective in the simulation of fsi problems with free surface flows and large structural displacements since the fluid boundaries are automatically defined by the position of the mesh nodes a distinctive feature of the proposed fsi strategy is that the solid domain is modelled using the explicit integration finite element method fem in a off the shelf commercial software abaqus explicit this allows to perform simulations with a complete and advanced description on the structural domain including advanced structural material models and contact the structure to fluid coupling algorithm is based on a technique derived from the domain decomposition methods namely the gravouil and combescure gc algorithm the method allows for arbitrarily large interface displacements using different time incrementation and non conforming meshes in the different domains which is an essential feature for the efficiency of an explicit solver involving different materials the resulting fully explicit and fully lagrangian finite element approach is particularly appealing for the possibility of its efficient application in a large variety of highly nonlinear engineering problems this article is protected by copyright all rights reserved

optimal switching over multiple regimes this paper studies the optimal switching problem for a general one dimensional diffusion with multiple more than two regimes this is motivated in the real options literature by the investment problem of a firm managing several production modes while facing uncertainties a viscosity solutions approach is employed to carry out a fine analysis on the associated system of variational inequalities leading to sharp qualitative characterizations of the switching regions these characterizations in turn reduce the switching problem into one of finding a finite number of threshold values in a state that would trigger switchings the results of our analysis take several qualitatively different forms depending on model parameters and the issue of when and where it is optimal to switch is addressed the general results are then demonstrated by the three regime case where a quasi explicit solution is obtained and a numerical procedure to find these critical values is devised in terms of the expectation functionals of hitting times for one dimensional diffusions

zero variance importance sampling estimators for markov process expectations we consider the use of importance sampling to compute expectations of functionals of markov processes for a class of expectations that can be characterized as positive solutions to a linear system we show there exists an importance measure that preserves the markovian nature of the underlying process and for which a zero variance estimator can be constructed the class of expectations considered includes expected infinite horizon discounted rewards as a particular case in this setting the zero variance estimator and associated importance measure can exhibit behavior that is not observed when estimating simpler path functionals like exit probabilities the zero variance estimators are not implementable in practice but their characterization can guide the design of a good importance measure and associated estimator by trying to approximate the zero variance ones we present bounds on the mean square error of such an approximate zero variance estimator based on lyapunov inequalities

unified lagrangian formulation for elastic solids and incompressible fluids application to fluid structure interaction problems via the pfem abstract we present a general lagrangian formulation for treating elastic solids and quasi fully incompressible fluids in a unified form the formulation allows to treat solid and fluid subdomains in a unified manner in fluid structure interaction fsi situations in our work the fsi problem is solved via the particle finite element method pfem the pfem is an effective technique for modeling complex interactions between floating and submerged bodies and free surface flows accounting for splashing of waves large motions of the bodies and frictional contact conditions applications of the unified lagrangian formulation to a number of fsi problems are given

the meshless finite element method a meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n and the condition that the shape functions depend only on the node positions furthermore the method proposed also shares several of the advantages of the finite element method such as a the simplicity of the shape functions in a large part of the domain b c0 continuity between elements which allows the treatment of material discontinuities and c ease of introduction of the boundary conditions copyright 2003 john wiley sons ltd

p1 p0 elements for incompressible flows with discontinuous material properties abstract we present a 3 noded triangle and a 4 noded tetrahedra with a continuous linear velocity and a discontinuous linear pressure field formed by the sum of an unknown constant pressure field and a prescribed linear field that satisfies the steady state momentum equations for a constant body force the elements are termed p1 p0 as the effective pressure field is linear although the unknown pressure field is piecewise constant within each element the elements have an excellent behavior for incompressible viscous flow problems with discontinuous material properties formulated in either eulerian or lagrangian descriptions the necessary numerical stabilization for dealing with the inf sup condition imposed by the incompressibility constraint and high convective effects in eulerian flows is introduced via the finite calculus fic approach for the sake of clarity the element derivation is presented first for the simpler stokes equations written in the standard eulerian frame the extension of the formulation to the navier stokes equations written in the eulerian and lagrangian frameworks is straightforward and is presented in the second part of the paper the efficiency and accuracy of the new p1 p0 triangle is verified by solving a set of incompressible multifluid flow problems using a lagrangian approach and a classical eulerian description the excellent performance of the new triangular element in terms of mass conservation and general accuracy for analysis of fluids with discontinuous material properties is highlighted

subdiffusion in a bounded domain with a partially absorbing reflecting boundary the exit time of a subdiffusive process from a bounded domain with a partially absorbing reflecting boundary is considered the short time and long time behaviors of the exit time probability density are investigated by using a spectral decomposition on the basis of the laplace operator eigenfunctions rotation invariant domains are analyzed in depth in order to illustrate the use of theoretical formulas and to compare them to numerical simulations the asymptotic results obtained are relevant for describing subdiffusion inside a living cell with a semipermeable membrane in a chemical reactor filled with catalytic grains of finite reactivity or in mineral or biological samples which are probed by nuclear magnetic resonance measurements subject to surface relaxation

a stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation abstract a stabilized finite element formulation for incompressible viscous flows is derived the starting point are the modified navier stokes equations incorporating naturally the necessary stabilization terms via a finite increment calculus fic procedure application of the standard finite element galerkin method to the modified differential equations leads to a stabilized discrete system of equations overcoming the numerical instabilities emanating from the advective terms and those due to the lack of compatibility between approximate velocity and pressure fields the fic method also provides a natural explanation for the stabilization terms appearing in all equations for both the navier stokes and the simpler stokes equations transient solution schemes with enhanced stabilization properties are also proposed finally a procedure for computing the stabilization parameters is presented

polyhedrization of an arbitrary 3d point set abstract given a 3d point set the problem of defining the volume associated dividing it into a set of regions elements and defining a boundary surface is tackled several physical problems need to define volume domains boundary surfaces and approximating functions from a given point distribution this is for instance the case of particle methods in which all the information is the particle positions and there are not boundary surfaces definition until recently all the fem mesh generators were limited to the generation of simple elements as tetrahedral or hexahedral elements or triangular and quadrangular in 2d problems the reason of this limitation was the lack of any acceptable shape function to be used in other kind of geometrical elements nowadays there are several acceptable shape functions for a very large class of polyhedra these new shape functions together with a generalization of the delaunay tessellation presented in this paper gives an optimal marriage and a powerful tool to solve a large variety of physical problems by numerical methods the domain partition into polyhedra presented here is not a standard mesh generation the problem here is for a given node distribution to find a suitable boundary surface and a suitable mesh to be used in the solution of a physical problem by a numerical method to include new nodes or change their positions is not allowed