Related papers: Averaging of semigroups associated to diffusion pr…
The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As well-known, the Gaussian transition probability density function (PDF) of this process is in conflict with…
In this paper we show that a process modeled by a strongly continuous real-valued semigroup (that has a space convolution operator as infinitesimal generator) cannot satisfy causality. We present and analyze a causal model of diffusion that…
This paper considers an $n$-particle jump-diffusion system with mean filed interaction, where the coefficients are locally Lipschitz continuous. We address the convergence as $n\to\infty$ of the empirical measure of the jump-diffusions to…
We show that for the mean zero simple exclusion process in $\mathbb {Z}^d$ and for the asymmetric simple exclusion process in $\mathbb{Z}^d$ for $d\geq3$, the self-diffusion coefficient of a tagged particle is stable when approximated by…
The aim of this paper is to study some continuous-time bivariate Markov processes arising from group representation theory. The first component (level) can be either discrete (quasi-birth-and-death processes) or continuous (switching…
Using the LePage representation, a strictly stable random element in a Banach space with $\alpha\in(0,2)$ can be represented as a sum of points of a Poisson process. This point process is union-stable, i.e. the union of its two independent…
We present a conception of the slow diffusion processes in the Euclidean spaces $\Bbb R^m, \; m\ge 1$, based on the theory of random flights with small constant speed that are driven by a homogeneous Poisson process of small rate. The slow…
In the presence of quantum measurements with direct photon detection the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, from these equations one can obtain diffusion models…
We simulated models of diffusion and aggregation in long pores of small widths in order to represent the basic mechanisms of coke deposition in catalysts' pores. Coke precursors are represented by particles injected at the pore entrance.…
It is known that the time until a birth and death process reaches a certain level is distributed as a sum of independent exponential random variables. Diaconis, Miclo and Swart gave a probabilistic proof of this fact by coupling the birth…
We present a systematic theory of dissipation in finite Fermi systems like nuclei and metallic clusters. This theory is based on the application of semiclassical methods and random matrix theory to linear response of many-body systems. The…
This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusion processes with killing on $[0,\infty)$. We obtain criteria for the exponential convergence to a unique quasi-stationary distribution in total…
Recent studies have shown that in the presence of noise both fronts propagating into a metastable state and so-called pushed fronts propagating into an unstable state, exhibit diffusive wandering about the average position. In this paper we…
We consider again the fast-slow motions setups in the continuous time $\frac {dX_N(t)}{dt}=N^{1/2} \sig(X_N(t))(\xi(tN))+b(X_N(t)),\, t\in [0,T]$ and the discrete time $X_N((n+1)/N)=X_N(n/N)+N^{-1/2}\sig(X_N(n/N))\xi(n)+N^{-1}b(X_N(n/N)),\,…
We propose a unified approach to establishing diffusion approximations for queues with impatient customers within a general framework of scaling customer patience time. The approach consists of two steps. The first step is to show that the…
We prove the convergence of the law of grid-valued random walks, which can be seen as time-space Markov chains, to the law of a general diffusion process. This includes processes with sticky features, reflecting or absorbing boundaries and…
We consider general Markov processes with absorption and provide criteria ensuring the exponential convergence in total variation of the distribution of the process conditioned not to be absorbed. The first one is based on two-sided…
We study a synchronous dispersion process in which $M$ particles are initially placed at a distinguished origin vertex of a graph $G$. At each time step, at each vertex $v$ occupied by more than one particle at the beginning of this step,…
In this short note we study homogenization of symmetric $d$-dimensional L\'evy processes. Homogenization of one-dimensional pure jump Markov processes has been investigated by Tanaka \emph{et al.} in 1992; their motivation was the work by…
In this paper, we aim to develop the averaging principle for a slow-fast system of stochastic reaction-diffusion equations driven by Poisson random measures. The coefficients of the equation are assumed to be functions of time, and some of…