Related papers: On absolute continuity of invariant measures assoc…
We define a general class of random systems of horizontal and vertical weighted broken lines on the quarter plane whose distribution are proved to be translation invariant. This invariance stems from a reversibility property of the model.…
We consider importance sampling as well as other properly weighted samples with respect to a target distribution $\pi$ from a different point of view. By considering the associated weights as sojourn times until the next jump, we define…
We consider zero-range processes in ${\mathbb{Z}}^d$ with site dependent jump rates. The rate for a particle jump from site $x$ to $y$ in ${\mathbb{Z}}^d$ is given by $\lambda_xg(k)p(y-x)$, where $p(\cdot)$ is a probability in…
In this paper we study splittings of a Poisson point process which are equivariant under a conservative transformation. We show that, if the Cartesian powers of this transformation are all ergodic, the only ergodic splitting is the obvious…
We study the long-term behavior of two piecewise-deterministic Markov processes used to model stochastic gene regulatory networks with bursting dynamics. Under regularity assumptions on the jump rate, we prove the existence and uniqueness…
We consider a class of observation-driven Poisson count processes where the current value of the accompanying intensity process depends on previous values of both processes. We show under a contractive condition that the bivariate process…
This paper is a step in the direction of understanding the behavior of non-intersecting Brownian motions on the real line, when the number of particles becomes large. Consider 2k non-intersecting Brownian motions, all starting at the…
This paper provides full classification of dynamics for continuous time Markov chains (CTMCs) on the non-negative integers with polynomial transition rate functions. Such stochastic processes are abundant in applications, in particular in…
We consider a simple discrete-time Markov chain with values in $[0,\infty)^{Z^d}$. The Markov chain describes various interesting examples such as oriented percolation, directed polymers in random environment, time discretizations of binary…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
In the paper, stationary measures of stochastic differential equations with jumps are considered. Under some general conditions, existence of stationary measures is proved through Markov measures and Lyapunov functions. Moreover, for two…
We propose a numerical method to approximate the value function for the optimal stopping problem of a piecewise deterministic Markov process (PDMP). Our approach is based on quantization of the post jump location---inter-arrival time Markov…
Piecewise-deterministic Markov processes (PDMPs) offer a powerful stochastic modeling framework that combines deterministic trajectories with random perturbations at random times. Estimating their local characteristics (particularly the…
We consider a stochastic process driven by a diffusion and jumps. We devise a technique, which is based on a discrete record of observations, for identifying the times when jumps larger than a suitably defined threshold occurred. The…
In previous publications, we showed that the incremental process of the chaotic diffusion of dissipative solitons in a prototypical complex Ginzburg-Landau equation, known, e.g., from nonlinear optics, is governed by a simple Markov process…
We register a random sequence which has the following properties: it has three segments being the homogeneous Markov processes. Each segment has his own one step transition probability law and the length of the segment is unknown and…
Motivated by stability questions on piecewise deterministic Markov models of bacterial chemotaxis, we study the long time behavior of a variant of the classic telegraph process having a non-constant jump rate that induces a drift towards…
IIn this paper, we study a partially observed progressive optimal control problem of forward-backward stochastic differential equations with random jumps, where the control domain is not necessarily convex, and the control variable enter…
We study a class of dynamical systems generated by random substitutions, which contains both intrinsically ergodic systems and instances with several measures of maximal entropy. In this class, we show that the measures of maximal entropy…
We define the probability structure of a continuous-time time-homogeneous Markov jump process, on a finite graph, that represents the continuous-time counterpart of the so-called Ruelle-Bowen discrete-time random walk. It constitutes the…