Related papers: Escape of mass in zero-range processes with random…
Let $E$ be a locally compact separable metric space and $m$ be a positive Radon measure on it. Given a nonnegative function $k$ defined on $E\times E$ off the diagonal whose anti-symmetric part is assumed to be less singular than the…
For a continuous-time random walk $X=\{X_t,t\ge 0\}$ (in general non-Markov), we study the asymptotic behavior, as $t\rightarrow \infty$, of the normalized additive functional $c_t\int_0^{t} f(X_s)ds$, $t\ge 0$. Similarly to the Markov…
Markov jump processes (MJPs) are used to model a wide range of phenomena from disease progression to RNA path folding. However, maximum likelihood estimation of parametric models leads to degenerate trajectories and inferential performance…
We study nearest-neighbors branching random walks started from a point at the interior of a hypercube. We show that the probability that the process escapes the hypercube is monotonically decreasing with respect to the distance of its…
In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference…
Given a sample from a discretely observed L\'evy process $X=(X_t)_{t\geq 0}$ of the finite jump activity, the problem of nonparametric estimation of the L\'evy density $\rho$ corresponding to the process $X$ is studied. An estimator of…
We investigate densities of vaguely continuous convolution semigroups of probability measures on $\mathbb{R}^d$. We expose that many typical conditions on the characteristic exponent repeatedly used in the literature of the subject are…
Consider compound Poisson processes with negative drift and no negative jumps, which converge to some spectrally positive L\'evy process with non-zero L\'evy measure. In this paper we study the asymptotic behavior of the local time process,…
Local perturbations in conservative particle systems can have a non-local influence on the stationary measure. To capture this phenomenon, we analyze in this paper two toy models. We study the symmetric exclusion process on a countable set…
The irreversible motion of an open quantum system can be represented through an ensemble of state vectors following a stochastic dynamics with piecewise deterministic paths. It is shown that this representation leads to a natural definition…
Given a discrete spatial structure $X$, we define continuous-time branching processes that model a population breeding and dying on $X$. These processes are usually called branching random walks. They are characterized by breeding rates…
Consider a tagged particle in zero-range dynamics on the integer lattice in dimension d with rate g whose finite-range jump probabilities p possess a drift. We show, in equilibrium, that the variance of the tagged particle position at time…
Using the matrix product formalism we formulate a natural p-species generalization of the asymmetric simple exclusion process. In this model particles hop with their own specific rate and fast particles can overtake slow ones with a rate…
We establish a sample path generation scheme in a unified manner for general multivariate infinitely divisible processes based on shot noise representation of their integrators. The approximation is derived from the decomposition of the…
Negative differential mobility is the phenomenon in which the velocity of a particle decreases when the force driving it increases. We study this phenomenon in Markov jump models where a particle moves in the presence of walls that act as…
It is well-known that 0 is the absorbing state for a branching system. Each particle in the system lives a random long time and gives a random number of new particles at its death time. It stops when the system has no particle. This paper…
The zero-range process is a stochastic interacting particle system that is known to exhibit a condensation transition. We present a detailed analysis of this transition in the presence of quenched disorder in the particle interactions.…
The discrete-time version of totally asymmetric simple-exclusion process (TASEP) on a finite one-dimensional lattice is studied with the periodic boundary condition. Each particle at a site hops to the next site with probability $0 \leq p…
We consider piecewise deterministic Markov processes with degenerate transition kernels of the "house-of-cards"-type. We use a splitting scheme based on jump times to prove the absolute continuity, as well as some regularity, of the…
We propose a definition o meta-stability and obtain sufficient conditions for a sequence of Markov processes on finite state spaces to be meta-stable. In the reversible case, these conditions reduce to estimates of the capacity and the…