S. G. Bobkov and C. Houdré recently posed the following question on the Internet (Problem posed in Stochastic Analysis Digest no. 15 (9/15/1995)): Let $X,Y$ be symmetric i.i.d. random variables such that $$P(|X+Y|/2 \geq t) \leq P(|X| \geq t),$$ for…

A comprehensive study of percolation in a more general context than the usual $Z^d$ setting is proposed, with particular focus on Cayley graphs, almost transitive graphs, and planar graphs. Results concerning uniqueness of infinite clusters and inequalities for the critical…

Exact expressions of the stochastic oscillatory integrals with the phase function, which is the quadratic Wiener functional obtained from the Malliavin derivative of the square norm of the Brownian sample path on interval, are given. As an application, the density…

In this paper we prove a strong approximation result for a mixing sequence with infinite variance and logarithmic decay rate of the mixing coefficient. The result is proved under the assumption that the distribution is symmetric and lies in the…

We give a simpler and shorter proof of Kesten's result for the probabilities with which a subordinator hits points.

Abstract. In this paper, we provide a characterization of a large class of transportation-cost inequalities in terms of exponential integrability of the cost function under the reference probability measure. Our results completely extend the previous works by Djellout, Guillin and…

A different but very short proof of a recent result of Khoshnevisan.

We construct examples of a random walk with pairwise-independent steps which is almost surely bounded, and for any m and k a random walk with k-wise independent steps which has no stationary distribution modulo m.

We build a Markovian system of particles entirely characterized by their masses, in which each pair of particles with masses $x$ and $y$ coalesce at rate $K(x,y)\simeq x^\lambda+y^\lambda$, for some $\lambda \in (0,1)$, and such that the system is initially…

Let $\mathbf{X}, \mathbf{X}_1, \mathbf{X}_2, ...$ be i.i.d. $\mathbb{R}^d$-valued random variables. We prove large and moderate deviations for Hotelling's $T^2$-statistic when $\mathbf{X}$ is in the generalized domain of attraction of the normal law.