Taking an odd, non-decreasing function [beta], we consider the (nonlinear) stochastic differential equation and we prove the existence and uniqueness of solution of Eq. E , where and (Bt; t[greater-or-equal, slanted]0) is a one-dimensional Brownian motion, B0=0. We show that Eq. E admits a...

The aim of this paper is to describe the minimum speed at which a super-Brownian motion starting at the Dirac mass at 0 moves away from its initial point. More precisely, we consider the class of functions and then determine the values of [kappa] such that the support of super-Brownian motion...

We consider the parametric estimation problem of intensity measure of a Poisson random measure. We prove large deviation principles for Poisson random measures and an implicit contraction principle. These results are applied to provide a large deviation principle for a maximum likelihood...

In this paper, the first part is concerned with the study of backward-forward stochastic differential equations without the non-degeneracy condition for the forward equation. We show existence and unicity of the solution to such equations under weaker monotonicity assumptions than those of Hu...

In this paper we extend the analysis in Benois et al. (Markov Process. Rel. Fields (1997) 175-198) by proving a strong large deviation principle for the empirical distribution of Ising spins in dimensions when the interaction is determined by a Kac potential and the temperature is below the...

We consider a càdlàg process the filtration generated by Y and generated by step processes Yn defined from Y by discretization in time. We study the stability in (with Skorokhod topology) of -martingales and of -solutions of related backward equations, when Yn--Y. We get this stability (in...

We study the almost sure asymptotic behaviour of decreasing stepsized stochastic algorithms used for the search of zeros of a function. We prove a law of the iterated logarithm, which gives the almost sure convergence rate of the algorithm, and we establish a quadratic strong law of large numbers.

We discuss the homogenization problem for a particular class of nested fractals, called "tree-like" Vicsek sets, which are not covered by the class considered in Kumagai and Kusuoka (1996). Random irreducible conductivities are assigned to each cell in the infinite fractal lattice and then we...

The existence and uniqueness of the solution of a backward SDE, on a random (possibly infinite) time interval, involving a subdifferential operator is proved. We then obtain a probabilistic interpretation for the viscosity solution of some parabolic and elliptic variational inequalities.

For {Xi}i = 1 a sequence of i.i.d. random variables taking values in a Polish space [Sigma] with distribution [mu], we obtain large and moderate deviation principles for the processes {n-1 [Sigma][nt]i = 1 [delta]Xi; t = 0}n = 1 and {n-1/2 [Sigma][nt]i = 1 ([delta]Xi - [mu]); t = 0}n = 1,...