Related papers: The exit-time problem for a Markov jump process

In this article, we consider time-inhomogeneous diffusive particle systems, whose particles jump from the boundary of a bounded open subset of $\R^d$, $d\geq 1$. We give a sufficient criterion for the family of empirical distributions of…

Incorporating boundary conditions into stochastic models of passive or active particle motion is usually implemented at the level of the associated forward or backward Kolmogorov equation, whose solution determines the probability…

We consider an optimal control problem for piecewise deterministic Markov processes (PDMPs) on a bounded state space. The control problem under study is very general: a pair of controls acts continuously on the deterministic flow and on the…

We consider the behaviour of branching-selection particle systems in the large population limit. The dynamics of these systems is the combination of the following three components: (a) Motion: particles move on the real line according to a…

Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a…

We study a one-dimensional Markov modulated random walk with jumps. It is assumed that amplitudes of jumps as well as a chosen velocity regime are random and depend on a time spent by the process at a previous state of the underlying Markov…

First exit times from regions and their dependence on variations of boundaries are discussed for diffusion processes. The paper presents an estimate of $L_1$-distance between exit times from two regions via expectations of exit times.

Understanding the time scales for diffusive processes and their degree of anisotropy is essential for modelling cosmic-ray transport in turbulent magnetic fields. We show that the diffusion time scales are isotropic over a large range of…

Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely…

A rescaled Markov chain converges uniformly in probability to the solution of an ordinary differential equation, under carefully specified assumptions. The presentation is much simpler than those in the outside literature. The result may be…

We consider the problem of non degenerate in energy metastable states forming a series in the framework of reversible finite state space Markov chains. We assume that starting from the state at higher energy the system necessarily visits…

We derive the Markov process equivalent to She-Leveque scaling in homogeneous and isotropic turbulence. The Markov process is a jump process for velocity increments $u(r)$ in scale $r$ in which the jumps occur randomly but with…

Consider a system of interacting particles indexed by the nodes of a graph whose vertices are equipped with marks representing parameters of the model such as the environment or initial data. Each particle takes values in a countable state…

We establish a recursive representation that fully decouples jumps from a large class of multivariate inhomogeneous stochastic differential equations with jumps of general time-state dependent unbounded intensity, not of L\'evy-driven type…

In this paper we develop a metastability theory for a class of stochastic reaction-diffusion equations exposed to small multiplicative noise. We consider the case where the unperturbed reaction-diffusion equation features multiple…

Diffusion processes have been applied with great success to model the dynamics of large populations throughout science, in particular biology. One advantage is that they bridge two different scales: the microscopic and the macroscopic one.…

This paper establishes limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamic coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump…

This paper analyses the impact of collisions in a system of $N$ identical hard-core particles driven according to a velocity jump process. The physical space is essentially a channel in $\mathbb{R}$ with a probability of occupants being…

The paper is concerned with the equilibrium distribution $\Pi_n$ of the $n$-th element in a sequence of continuous-time density dependent Markov processes on the integers. Under a $(2+\a)$-th moment condition on the jump distributions, we…

We study the nonlocal Stefan problem, where the phase transition is described by a nonlocal diffusion as well as the change of enthalpy functions. By using a stochastic optimization approach introduced for the local case, we construct…