Related papers: Approximation of the Exit Probability of a Stable …

Let $E$ be a finite set, $\{F^i\}_{i \in E}$ a family of vector fields on $\mathbb{R}^d$ leaving positively invariant a compact set $M$ and having a common zero $p \in M.$ We consider a piecewise deterministic Markov process $(X,I)$ on $M…

We consider a Markov chain $(M_{n})_{n\ge 0}$ on the set $\mathbb{N}_{0}$ of nonnegative integers which is eventually decreasing, i.e. $\mathbb{P}\{M_{n+1}<M_{n}|M_{n}\ge a\}=1$ for some $a\in\mathbb{N}$ and all $n\ge 0$. We are interested…

Suppose X and Y are two independent irreducible Markov chains on n states. We consider the intersection time, which is the first time their trajectories intersect. We show for reversible and lazy chains that the total variation mixing time…

We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…

We consider a discrete-time two-dimensional process $\{(X_{1,n},X_{2,n})\}$ on $\mathbb{Z}^2$ with a background process $\{J_n\}$ on a finite set $S_0$, where individual processes $\{X_{1,n}\}$ and $\{X_{2,n}\}$ are both skip free. We…

We consider the random walk Metropolis algorithm on $\mathbb{R}^n$ with Gaussian proposals, and when the target probability measure is the $n$-fold product of a one-dimensional law. In the limit $n\to\infty$, it is well known (see [Ann.…

Many systems across the sciences evolve through a combination of multiplicative growth and diffusive transport. In the presence of disorder, these systems tend to form localized structures which alternate between long periods of relative…

We study a variant of the Generalized Excited Random Walk (GERW) on $\mathbb{Z}^d$ introduced by Menshikov, Popov, Ram\'irez and Vachkovskaia in [Ann. Probab. 40 (5), 2012]. It consists of a particular version of the model studied in [arXiv…

We consider weighted graphs satisfying sub-Gaussian estimate for the natural random walk. On such graphs, we study symmetric Markov chains with heavy tailed jumps. We establish a threshold behavior of such Markov chains when the index…

Tandem queueing networks are widely used to model systems where services are provided in sequential stages. In this study, we assume that each station in the tandem system operates under a general renewal process. Additionally, we assume…

We derive an approximate but explicit formula for the Mean First Passage Time of a random walker between a source and a target node of a directed and weighted network. The formula does not require any matrix inversion, and it takes as only…

We prove a quenched central limit theorem for random walks with bounded increments in a randomly evolving environment on $\mathbb{Z}^d$. We assume that the transition probabilities of the walk depend not too strongly on the environment and…

We consider the process $\{x-N(t):t\geq 0\}$, where $x\in\mathbb{R}_+$ and $\{N(t):t\geq 0\}$ is a renewal process with light-tailed distributed holding times. We are interested in the joint distribution of $(\tau(x),A(x))$ where $\tau(x)$…

Let $\{X_n\}_{n\in\N}$ be a Markov chain on a measurable space $\X$ with transition kernel $P$ and let $V:\X\r[1,+\infty)$. The Markov kernel $P$ is here considered as a linear bounded operator on the weighted-supremum space $\cB_V$…

The cutoff phenomenon describes a sharp transition in the convergence of a family of ergodic finite Markov chains to equilibrium. Many natural families of chains are believed to exhibit cutoff, and yet establishing this fact is often…

We consider dynamical percolation on the complete graph $K_n$, where each edge refreshes its state at rate $\mu \ll 1/n$, and is then declared open with probability $p = \lambda/n$ where $\lambda > 1$. We study a random walk on this…

We address a class of Markov jump linear systems that are characterized by the underlying Markov process being time-inhomogeneous with a priori unknown transition probabilities. Necessary and sufficient conditions for uniform stochastic…

We consider the problem of bounding mean first passage times for a class of continuous-time Markov chains that captures stochastic interactions between groups of identical agents. The quantitative analysis of such probabilistic population…

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMP's) taking values in a general Borel space and with compact action space depending on the state variable. The control…

In this note we derive the exact probability that a specific state in a two-state Markov chain is visited exactly $k$ times after $N$ transitions. We provide a closed-form solution for $\mathbb{P}(N_l = k \mid N)$, considering initial state…