Related papers: Joint Hitting-Time Densities for Finite State Mark…

We consider a Markov process $X$, which is the solution of a stochastic differential equation driven by a L\'{e}vy process $Z$ and an independent Wiener process $W$. Under some regularity conditions, including non-degeneracy of the…

We study an infinite system of moving particles, where each particle is of type A or B. Particles perform independent random walks at rates D_A>0 and D_B>0, and the interaction is given by mutual annihilation A+B->0. The initial condition…

In this second part, we analyze the dissipation properties of Generalized Poisson-Kac (GPK) processes, considering the decay of suitable $L^2$-norms and the definition of entropy functions. In both cases, consistent energy dissipation and…

This article analyzes the formulation of space-time continuous hyperbolic hydrodynamic models for systems of interacting particles moving on a lattice, by connecting their local stochastic lattice dynamics to the formulation of an…

We study discrete-time, discrete-state multistate Markov models from the perspective of algebraic statistics. These models are widely studied in event history analysis, and are characterized by the state space, the initial distribution and…

Consider a compact metric space $S$ and a pair $(j,k)$ with $k \ge 2$ and $1 \le j \le k$. For any probability distribution $\theta \in P(S)$, define a Markov chain on $S$ by: from state $s$, take $k$ i.i.d. ($\theta$) samples, and jump to…

We make use of the Open Quantum Random Walk setting due to S. Attal, F. Petruccione, C. Sabot and I. Sinayskiy [J. Stat. Phys. (2012) 147:832-852] in order to discuss hitting times and a quantum version of the Mean Hitting Time Formula from…

Let (Xt, t >= 0) be a diffusion process with jumps, sum of a Brownian motion with drift and a compound Poisson process. We consider T_x the first hitting time of a fixed level x > 0 by (Xt, t >= 0). We prove that the law of T_x has a…

We revise the classical problem of characterizing first exit times of a harmonically trapped particle whose motion is described by one- or multi-dimensional Ornstein-Uhlenbeck process. We start by recalling the main derivation steps of a…

We derive some key extremal features for $k$th order Markov chains that can be used to understand how the process moves between an extreme state and the body of the process. The chains are studied given that there is an exceedance of a…

We present a numerical method to compute the survival function and the moments of the exit time for a piecewise-deterministic Markov process (PDMP). Our approach is based on the quantization of an underlying discrete-time Markov chain…

In this paper, we consider a homogeneous Markov process \xi(t;\omega) on an ultrametric space Q_p, with distribution density f(x,t), x in Q_p, t in R_+, satisfying the ultrametric diffusion equation df(x,t)/dt =-Df(x,t). We construct and…

We consider irreversible Markov chains on finite commutative rings randomly generated using both addition and multiplication. We restrict ourselves to the case where the addition is uniformly random and multiplication is arbitrary. We first…

First passage of stochastic processes under resetting has recently been an active research topic in the field of statistical physics. However, most of previous studies mainly focused on the systems with continuous time and space. In this…

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…

We study the density of states (DOS) for disordered systems whose spectral statistics can be described by a Gaussian ensemble of almost diagonal Hermitian random matrices. The matrices have independent random entries $ H_{i \geq j} $ with…

Consider a Markov chain $\{X_n\}_{n\ge 0}$ with an ergodic probability measure $\pi$. Let $\Psi$ a function on the state space of the chain, with $\alpha$-tails with respect to $\pi$, $\alpha\in (0,2)$. We find sufficient conditions on the…

We study K-processes, which are Markov processes in a denumerable state space, all of whose elements are stable, with the exception of a single state, starting from which the process enters finite sets of stable states with uniform…

We propose a method for approximating solutions to optimization problems involving the global stability properties of parameter-dependent continuous-time autonomous dynamical systems. The method relies on an approximation of the…

We consider a transitive action of a finitely generated group $G$ and the Schreier graph $\Gamma$ defined by this action for some fixed generating set. For a probability measure $\mu$ on $G$ with a finite first moment we show that if the…