Related papers: An Overshoot Approach to Recurrence and Transience…

For any two-sided jumping $\alpha$-stable process, where $1 < \alpha < 2$, we find an explicit identity for the law of the first hitting time of the origin. This complements existing work in the symmetric case and the spectrally one-sided…

We consider a branching stable process with positive jumps, i.e. a continuous-time branching process in which the particles evolve independently as stable L{\'e}vy processes with positive jumps. Assuming the branching mechanism is critical…

Let $(M,d,\mu)$ be a uniformly discrete metric measure space satisfying space homogeneous volume doubling condition. We consider discrete time Markov chains on $M$ symmetric with respect to $\mu$ and whose one-step transition density is…

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…

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…

Renewal processes are zero-dimensional processes defined by independent intervals of time between zero crossings of a random walker. We subject renewal processes them to stochastic resetting by setting the position of the random walker to…

We consider a discrete time population model for which each individual alive at time $n$ survives independently of everybody else at time $n+1$ with probability $\beta_n$. The sequence $(\beta_n)$ is i.i.d. and constitutes our random…

We introduce an extension to the standard reduction of oscillatory systems to a single phase variable. The standard reduction is often insufficient, particularly when the oscillations have variable amplitude and the magnitude of each…

This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the…

It is shown that transient graphs for the simple random walk do not admit a nearest neighbor transient Markov chain (not necessarily a reversible one), that crosses all edges with positive probability, while there is such chain for the…

An up-down chain is a Markov chain in which each transition is a two-step process that moves up to a larger object and then back down to an object of the original size. The first goal of this paper is to present a general framework for…

The present paper extends the earlier results obtained by Abramov [`Conditions for recurrence and transience for time-inhomogeneous birth-and-death processes' \emph{Bull. Aust. Math. Soc.} \textbf{109} (2024), 393--402] for the case of…

In the article the distributions of overjump functionals for almost semi-continuous processes on a finite irreducible Markov chain are considered.

We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…

In Markov networks, measurement blackouts with unknown frequency compromise observations such that thermodynamic quantities can no longer be inferred reliably. In particular, the observed currents neither discern equilibrium from…

We consider a continuous-time vertex reinforced jump process on a supercritical Galton-Watson tree. This process takes values in the set of vertices of the tree and jumps to a neighboring vertex with rate proportional to the local time at…

This work continues and substantially extends our recent work on switching diffusions with the switching processes that depend on the past states and that take values in a countable state space. That is, the discrete components of the…

Let G \subset \R^k be a convex polyhedral cone with vertex at the origin given as the intersection of half spaces {G_i, i= 1, ..., N}, where n_i and d_i denote the inward normal and direction of constraint associated with G_i, respectively.…

We consider a system of $N$ particles interacting through their empirical distribution on a finite state space in continuous time. In the formal limit as $N\to\infty$, the system takes the form of a nonlinear (McKean--Vlasov) Markov chain.…

We extend the Dirichlet principle to non-reversible Markov processes on countable state spaces. We present two variational formulas for the solution of the Poisson equation or, equivalently, for the capacity between two disjoint sets. As an…