The 36th Séminaire de Probabilités contains an advanced course on Logarithmic Sobolev Inequalities by A. Guionnet and B. Zegarlinski, as well as two shorter surveys by L. Pastur and N. O'Connell on the theory of random matrices and their links with stochastic processes. The main themes of the other contributions are Logarithmic Sobolev Inequalities, Stochastic Calculus, Martingale Theory and Filtrations. Besides the traditional readership of the Séminaires, this volume will be useful to researchers in statistical mechanics and mathematical finance.

The 37th SA(c)minaire de ProbabilitA(c)s contains A. Lejay's advanced course which is a pedagogical introduction to works by T. Lyons and others on stochastic integrals and SDEs driven by deterministic rough paths. The rest of the volume consists of various articles on topics familiar to regular readers of the SA(c)minaires, including Brownian motion, random environment or scenery, PDEs and SDEs, random matrices and financial random processes.

The volume consists entirely of research papers, principally in stochastic calculus, martingales, and Brownian motion, and gathers an important part of the works done in the main probability groups in France (Paris, Strasbourg, Toulouse, Besan on, Grenoble, ...) together with closely related works done by some probabilists elsewhere (Switzerland, India, Austria, ...)

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.

In this volume of original research papers, the main topics discussed relate to the asymptotic windings of planar Brownian motion, structure equations, closure properties of stochastic integrals. The contents of the volume represent an important fraction of research undertaken by French probabilists and their collaborators from abroad during the academic year 1992-1993.

All the papers included in this volume are original research papers. They represent an important part of the work of French probabilists and colleagues with whom they are in close contact throughout the world. The main topics of the papers are martingale and Markov processes studies.

All the papers contained in the volume are original, fully refereed researchpapers. They represent a fairly broad spectrum of the research activity in probability theory, which was done internationally in 1990-1991, with particular emphasis on Markov processes and stochastic calculus. The latter subject keeps growing, and some important new developments, included in the volume, concern anticipative stochastic integrals, and new applications of the enlargements of filtrations to the study of zeros of martingales. FROM THE CONTENTS: R. Bass, D. Khoshnevisan: Stochastic calculus and the continuity of local times of Levy processes.- M.T. Barlow, P. Imkeller: On some sample path properties of Skorokhod integral processes.- T.S. Mountford: A critical function for the planar Brownian convex hull.- L. Dubins, M. Smorodinsky: The modified, discrete Levy transformation is Bernoulli.- M. Baxter: Markov processes on the boundary of the binary tree.- R. Abraham: Unarbre aleatoire infini associe a l'excursion brownienne.- S.E. Kuznetsov: On the existence of a dual semigroup.

All the papers in the volume are original research papers, discussing fundamental properties of stochastic processes. The topics under study (martingales, filtrations, path properties, etc.) represent an important part of the current research performed in 1996-97 by various groups of probabilists in France and abroad.

The different papers contained in this volume are all research papers. The main directions of research which are being developed are: quantum probability, semimartingales and stochastic calculus.

Besides a number of papers on classical areas of research in probability such as martingale theory, Malliavin calculus and 2-parameter processes, this new volume of the S minaire de Probabilit?'s develops the following themes: - chaos representation for some new kinds of martingales, - quantum probability, - branching aspects on Brownian excursions, - Brownian motion on a set of rays.