In the present paper we compute the laws of some functionals of doubly perturbed Brownian motion, which is the solution of the equation Xt=Bt+[alpha] sups[less-than-or-equals, slant]t Xs+[beta] infs[less-than-or-equals, slant]t Xs, where [alpha],[beta]1, and B is a real Brownian motion. We first...

We use martingale methods to obtain an explicit formula for the expected wet period of the finite dam of capacity V, where the amounts of inputs are i.i.d exponential random variables and the output rate is one, when the reservoir is not empty. As a consequence, we obtain an explicit formula for...

We prove a strong approximation for the spatial Kesten-Spitzer random walk in random scenery by a Wiener process.

We consider the Glauber and Kawasaki dynamics for the Blume-Capel spin model with weak long-range interaction on the infinite lattice: a ferromagnetic d-dimensional lattice system with the spin variable [sigma] taking values in {-1,0,1} and pair Kac potential . The Kawasaki dynamics conserves...

The paper establishes strong convergence results for the joint convergence of sequential order statistics. There exists an explicit construction such that almost sure convergence to extremal processes follows. If a partial sum of rowwise i.i.d. random variables is attracted by a non-Gaussian...

Suppose given a realization of a Poisson process on the line: call the points 'germs' because at a given instant 'grains' start growing around every germ, stopping for any particular grain when it touches another grain. When all growth stops a fraction e-1 of the line remains uncovered. Let n...

A numerical scheme for stochastic differential equations with convex constraints is considered. The solutions to the SDEs are constrained to the domain of convex lower semicontinuous function through a multivalued monotone drift component and a variational inequality. The projection scheme is a...

Given a stationary differentiable in probability process we express the asymptotic behaviour of the tail P{supt[set membership, variant][0,1] [xi](t)u} for large u through a certain functional of the conditional law ([xi]'(1)[xi](1)u). Under technical conditions this functional becomes the...

The paper deals with a path-valued Markov process: the reflecting Brownian snake. It is a particular case of the path-valued process previously introduced by Le Gall. Here the spatial motion is a reflecting Brownian motion in a domain D of . Using this probabilistic tool, we construct an...

We present a weighted sampling Moran particle system model for the numerical solving of a class of Feynman-Kac formulae which arise in different fields. Our major motivation was from nonlinear filtering, but our approach is context free. We will show that under certain regularity conditions the...