For a bivariate Lévy process ([xi]t,[eta]t)t=0 the generalised Ornstein-Uhlenbeck (GOU) process is defined as where . We define necessary and sufficient conditions under which the infinite horizon ruin probability for the process is zero. These conditions are stated in terms of the canonical...

We present a model for random transport along periodic two-dimensional flows and use the concept of rotation numbers from dynamical systems to prove a functional central limit theorem for this model. The limiting law turns out to be a stable Lévy process.

We estimate a median of f(Xt) where f is a Lipschitz function, X is a Lévy process and t is an arbitrary time. This leads to concentration inequalities for f(Xt). In turn, corresponding fluctuation estimates are obtained under assumptions typically satisfied if the process has a regular...

This paper discusses the existence of gradient estimates for the heat kernel of a second order hypoelliptic operator on a manifold. For elliptic operators, it is now standard that such estimates (satisfying certain conditions on coefficients) are equivalent to a lower bound on the Ricci tensor...

Let G={G(x),x[set membership, variant]R1} be a mean zero Gaussian process with stationary increments and set [sigma]2(x-y)=E(G(x)-G(y))2. Let f be a symmetric function with Ef2([eta])[infinity], where [eta]=N(0,1). When [sigma]2(s) is concave or when [sigma]2(s)=sr, 1r=3/2, where...

Upsilon transformations satisfying certain regularity conditions are shown to generate semigroups of such transformations. This is based on a general commutativity property of the Upsilon transformations, and uses log infinite divisibility. The existence of random integral representations of...

In this article, we study the family of probability measures (indexed by ), obtained by penalization of the Brownian motion with a given functional of its local times at time t. We prove that this family tends to a limit measure when t goes to infinity if the functional satisfies some conditions...

We consider a one-dimensional dynamical system driven by a vector field -U', where U is a multi-well potential satisfying some regularity conditions. We perturb this dynamical system by a stable symmetric non-Gaussian Lévy process whose scale decreases as a power function of time. It turns out...

We consider a real Gaussian process X with unknown smoothness where the mean square derivative X(r0) is supposed to be Hölder continuous in quadratic mean. First, from selected sampled observations, we study the reconstruction of X(t), t[set membership, variant][0,1], with a piecewise...

Consider a continuous analogue of the simulated annealing algorithm in , namely the solution of the SDE , where V is a function called the potential. We prove a convergence result, similar to the one in [L. Miclo, Thèse de doctorat, Ph.D. Thesis, Université Paris VI, 1991], under weaker...