We study the Euler scheme for a stochastic differential equation driven by a Lévy process Y . More precisely, we look at the asymptotic behavior of the normalized error process un(X −X), where X is the true solution and X is its Euler approximation with stepsize 1/n, and un is an appropriate rate going to infinity: if the normalized error processes converge, or are at least tight, we say that t...

We obtain the asymptotics for the speed of a particular case of a particle system with branching and selection introduced by Bérard and Gouéré (2010). The proof is based on a connection with a supercritical Galton-Watson process censored at a certain level. Résumé Nous étudions un cas particulier de système de particules avec branchement et sélection introduit par Bérard et Gouéré (2010). Nous ...

We introduce a new family of probability distributions on the set of pure states of a finite dimensional quantum system. Without any a priori assumptions, the most natural measure on the set of pure state is the uniform (or Haar) measure. Our family of measures is indexed by a time parameter t and interpolates between a deterministic measure (t = 0) and the uniform measure (t = ∞). The measures...