Seminaire de Probabilites XXXI

The 31 papers collected here present original research results obtained in 1995-96, on Brownian motion and, more generally, diffusion processes, martingales, Wiener spaces, polymer measures.

Branching processes, the Ray-Knight theorem, and sticky Brownian motion.- Integration by parts and Cameron-Martin formulas for the free path space of a compact Riemannian manifold.- The change of variables formula on Wiener space.- Classification des Semi-Groupes de diffusion sur IR associés à une famille de polynômes orthogonaux.- A differentiable isomorphism between Wiener space and path group.- On martingales which are finite sums of independent random variables with time dependent coefficients.- Oscillation presque sûre de martingales continues.- A note on Cramer’s theorem.- The hypercontractivity of Ornstein-Uhlenbeck semigroups with drift, revisited.- Une preuve standard du principe d’invariance de stoll.- Marches aléatoires auto-évitantes et mesures de polymère.- On the tails of the supremum and the quadratic variation of strictly local martingales.- On Wald’s equation. Discrete time case.- Remarques sur l’hypercontractivité et l’évolution de l’entropie pour des chaînes de Markov finies.- Comportement des temps d’atteinte d’une diffusion fortement rentrante.- Closed sets supporting a continuous divergent martingale.- Some polar sets for the Brownian sheet.- A counter-example concerning a condition of Ogawa integrability.- The multiplicity of stochastic processes.- Theoremes limites pour les temps locaux d’un processus stable symetrique.- An Itô type isometry for loops in Rd via the Brownian bridge.- On continuous conditional Gaussian martingales and stable convergence in law.- Simple examples of non-generating Girsanov processes.- Formule d’Ito généralisée pour le mouvement brownien linéaire.- On the martingales obtained by an extension due to Saisho, Tanemura and Yor of Pitman’s theorem.- Some remarks on Pitman’s theorem.-On the lengths of excursions of some Markov processes.- On the relative lengths of excursions derived from a stable subordinator.- Some remarks about the joint law of Brownian motion and its supremum.- A characterization of Markov solutions for stochastic differential equations with jumps.- Diffeomorphisms of the circle and the based stochastic loop space.- Vitesse de convergence en loi pour des solutions d’équations différentielles stochastiques vers une diffusion.- Projection d’une diffusion réelle sur sa filtration lente.