We construct a stochastic process whose drift is a function of the process's local time at a reflecting barrier. The process arose as a model of the interactions of a Brownian particle and an inert particle in a paper by…

Under the hypothesis of convergence in probability of a sequence of càdlàg processes $(X^n)$ to a càdlàg process $X$, we are interested in the convergence of corresponding values in optimal stopping and also in the convergence of optimal stopping times.…

For a symmetric random walk in $Z^2$ which does not necessarily have bounded jumps we study those points which are visited an unusually large number of times. We prove the analogue of the Erdös-Taylor conjecture and obtain the asymptotics for…

We resolve the longstanding question of how to define the compensator of a point process on a general partially ordered set in such a way that the compensator exists, is unique, and characterizes the law of the process. We define…

In the supermarket model there are $n$ queues, each with a unit rate server. Customers arrive in a Poisson process at rate $\lambda n$, where $0<\lambda<1$. Each customer chooses $d \geq 2$ queues uniformly at random, and joins a shortest…

Our first aim in this paper is to characterize Palm measures of stationary point processes through point stationarity. This generalizes earlier results from the Euclidean case to the case of an Abelian group. While a stationary point process looks statistically…

Stable non-Gaussian self-similar mixed moving averages can be decomposed into several components. Two of these are the periodic and cyclic fractional stable motions which are the subject of this study. We focus on the structure of their integral representations and…

A Bernoulli random walk is a random trajectory starting from 0 and having i.i.d. increments, each of them being +1 or -1, equally likely. The other families quoted in the title are Bernoulli random walks under various conditions. A peak…

Consider the high-order heat-type equation $\partial u/\partial t=\pm\partial^N u/\partial x^N$ for an integer $N>2$ and introduce the related Markov pseudo-process $(X(t))_{t\ge 0}$. In this paper, we study several functionals related to $(X(t))_{t\ge 0}$: the maximum $M(t)$ and minimum $m(t)$ up…

We study regularizing properties for transition semigroups related to Ornstein Uhlenbeck processes with values in a Banach space $E$ which is continuously and densely embedded in a real and separable Hilbert space $H$. Namely we study conditions under which the…