We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, a regular explicit Euler scheme-with constant or decreasing step-may explode and implicit Euler schemes are CPU-time expensive. The algorithm we...

We prove the weak convergence in of the laws of the Itô and Stratonovich multiple integrals of some classes of deterministic functions with respect to the fractional Brownian motion, BH, with Hurst parameter H1/2, to the law of the corresponding multiple integral with respect to BH0, when H...

In this note we consider a chain of N oscillators, whose ends are in contact with two heat baths at different temperatures. Our main result is the exponential convergence to the unique invariant probability measure (the stationary state). We use the Lyapunov's function technique of Rey-Bellet...

In this paper we carry over the concept of reverse probabilistic representations developed in Milstein, Schoenmakers, Spokoiny [G.N. Milstein, J.G.M. Schoenmakers, V. Spokoiny, Transition density estimation for stochastic differential equations via forward-reverse representations, Bernoulli 10...

We consider the height process of a Lévy process with no negative jumps, and its associated continuous tree representation. Using tools developed by Duquesne and Le Gall, we construct a fragmentation process at height, which generalizes the fragmentation at height of stable trees given by...

A local strict comparison theorem and some converse comparison theorems are proved for reflected backward stochastic differential equations under suitable conditions.

Let X be a multidimensional diffusion with jumps. We provide sets of conditions under which: X fulfils the ergodic theorem for any initial distribution; and X is exponentially [beta]-mixing. Utilizing the Foster-Lyapunov drift criteria developed by Meyn and Tweedie, we extend several existing...

Let [Xi] be the set of points (we call the elements of [Xi] centers) of a Poisson process in , d=2, with unit intensity. Consider the allocation of to [Xi] which is stable in the sense of the Gale-Shapley marriage problem and in which each center claims a region of volume [alpha]=1. We prove...

A multivariate Lévy-driven continuous time autoregressive moving average (CARMA) model of order (p,q), qp, is introduced. It extends the well-known univariate CARMA and multivariate discrete time ARMA models. We give an explicit construction using a state space representation and a spectral...

In this paper, by using a Taylor type development, we show how it is possible to associate differential operators with stochastic differential equations driven by fractional Brownian motions. As an application, we deduce that invariant measures for such SDE's must satisfy an infinite dimensional...