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In this article, we define the new concept of local coupling property for Markov processes and study its relationship with distributional properties of the transition probability. In the special case of L\'evy processes we show that this…
We construct the analogue of the local time -- at a fixed point $x$ -- for Markov processes indexed by Levy trees. We start by proving that Markov processes indexed by Levy trees satisfy a special Markov property which can be thought as a…
We consider a continuous-time random walk which is defined as an interpolation of a random walk on a point process on the real line. The distances between neighboring points of the point process are i.i.d. random variables in the normal…
The escape from a given domain is one of the fundamental problems in statistical physics and the theory of stochastic processes. Here, we explore properties of the escape of an inertial particle driven by L\'evy noise from a bounded domain,…
Random Bridges have gained significant attention in recent years due to their potential applications in various areas, particularly in information-based asset pricing models. This paper aims to explore the potential influence of the pinning…
For non-Gaussian stochastic dynamical systems, mean exit time and escape probability are important deterministic quantities, which can be obtained from integro-differential (nonlocal) equations. We develop an efficient and convergent…
Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of L\'evy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker,…
Systems of stochastic particles evolving in a multi-well energy landscape and attracted to their barycenter is the prototypical example of mean-field process undergoing phase transitions: at low temperature, the corresponding mean-field…
We consider a piecewise-deterministic Markov process governed by a jump intensity function, a rate function that determines the behaviour between jumps, and a stochastic kernel describing the conditional distribution of jump sizes. We study…
In this paper we study coupled fully non-local equations, where a linear non-local operator jointly acts on the time and space variables. We establish existence and uniqueness of the solution. A maximum principle is proved and used to…
The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous…
In this note we consider a Markov chain formed by a finite system of interacting birth-and-death processes on a finite state space. We study an asymptotic behaviour of the Markov chain as its state space becomes large. In particular, we…
We show the existence of L\'evy-type stochastic processes in one space dimension with characteristic triplets that are either discontinuous at thresholds, or are stable-like with stability index functions for which the closures of the…
A Levy walk is a non-Markovian stochastic process in which the elementary steps of the walker consist of motion with constant speed in randomly chosen directions and for a random period of time. The time of flight is chosen from a…
Markov automata combine non-determinism, probabilistic branching, and exponentially distributed delays. This compositional variant of continuous-time Markov decision processes is used in reliability engineering, performance evaluation and…
We develop criteria for recurrence and transience of one-dimensional Markov processes which have jumps and oscillate between $+\infty$ and $-\infty$. The conditions are based on a Markov chain which only consists of jumps (overshoots) of…
This paper is devoted to the problem of sample path large deviations for the Markov processes on R_+^N having a constant but different transition mechanism on each boundary set {x:x_i=0 for i\notin\Lambda, x_i>0 for i\in\Lambda}. The global…
We consider a continuous-time Markov chain with a finite or countable state space. For a site y and subset H of the state space, the hitting time of y under taboo H is defined to be infinite if the process trajectory hits H before y, and…
Continuous-time Markov decision processes are an important class of models in a wide range of applications, ranging from cyber-physical systems to synthetic biology. A central problem is how to devise a policy to control the system in order…
The notion of a successful coupling of Markov processes, based on the idea that both components of the coupled system ``intersect'' in finite time with probability one, is extended to cover situations when the coupling is unnecessarily…