This paper studies particle propagation in a one-dimensional inhomogeneous medium where the laws of motion are generated by chaotic and deterministic local maps. Assuming that the particle’s initial location is random and uniformly distributed, this dynamical system can be reduced to a random...

We construct a weak solution to the stochastic functional differential equation Xt=x0+∫0tσ(Xs,Ms)dWs, where Mt=sup0≤s≤tXs. Using the excursion theory, we then solve explicitly the following problem: for a natural class of joint density functions μ(y,b), we specify σ(.,.), so that X is a...

Based on an R2-valued random sample {(yi,xi),1≤i≤n} on the simple linear regression model yi=xiβ+α+εi with unknown error variables εi, least squares processes (LSPs) are introduced in D[0,1] for the unknown slope β and intercept α, as well as for the unknown β when α=0. These LSPs...

In this paper we study the integral–partial differential equations of Isaacs’ type by zero-sum two-player stochastic differential games (SDGs) with jump-diffusion. The results of Fleming and Souganidis (1989) [9] and those of Biswas (2009) [3] are extended, we investigate a controlled...

Constrained diffusions, with diffusion matrix scaled by small ϵ0, in a convex polyhedral cone G⊂Rk, are considered. Under suitable stability assumptions small noise asymptotic properties of invariant measures and exit times from domains are studied. Let B⊂G be a bounded domain. Under...

We study sequences of empirical measures of Euler schemes associated to some non-Markovian SDEs: SDEs driven by Gaussian processes with stationary increments. We obtain the functional convergence of this sequence to a stationary solution to the SDE. Then, we end the paper by some specific...

The stability and ergodicity properties of two adaptive random walk Metropolis algorithms are considered. Both algorithms adjust the scaling of the proposal distribution continuously based on the observed acceptance probability. Unlike the previously proposed forms of the algorithms, the adapted...

We study the exact asymptotics of , as u--[infinity], where and {Z(t):t=0} is a centered stationary Gaussian process with covariance function satisfying some regularity conditions. As an application, we analyze the probability of buffer emptiness in a Gaussian fluid queueing system and the...

Consider an independent site percolation model with parameter p[set membership, variant](0,1) on , where there are only nearest neighbor bonds and long range bonds of length k parallel to each coordinate axis. We show that the percolation threshold of such a model converges to when k goes to...

Given an observation of the uniform empirical process [alpha]n, its functional increments [alpha]n(u+an[dot operator])-[alpha]n(u) can be viewed as a single random process, when u is distributed under the Lebesgue measure. We investigate the almost sure limit behaviour of the multivariate...