Bøger i Seminaire de Probabilites serien i rækkefølge

Twenty-five articles have been selected from the first 14 volumes of the "Séminaire de Probabilités", all out of print, for their historical and/or mathematical interest. Among the many articles devoted to Martingale theory in the early volumes of the Séminaire, we have chosen to reprint those that are particularly significant from a historical point of view, as well as those that can still be useful today. They are reprinted here verbatim, with a short retrospective comment, for the benefit of researchers in the theory of stochastic processes, in mathematical finance, or in history of mathematics.

This volume presents a selection of texts that reflects the current research streams in probability, with an interest toward topics such as filtrations, Markov processes and Markov chains as well as large deviations, Stochastic Partial Differential equations, rough paths theory, quantum probabilities and percolation on graphs.The featured contributors are R. L. Karandikar and B. V. Rao, C. Leuridan, M. Vidmar, L. Miclo and P. Patie, A. Bernou, M.-E. Caballero and A. Rouault, J. Dedecker, F. Merlevède and E. Rio, F. Brosset, T. Klein, A. Lagnoux and P. Petit, C. Marinelli and L. Scarpa, C. Castaing, N. Marie and P. Raynaud de Fitte, S. Attal, J. Deschamps and C. Pellegrini, and N. Eisenbaum.

As usual, some of the contributions to this 44th Séminaire de Probabilités were presented during the Journées de Probabilités held in Dijon in June 2010. The remainder were spontaneous submissions or were solicited by the editors. The traditional and historical themes of the Séminaire are covered, such as stochastic calculus, local times and excursions, and martingales. Some subjects already touched on in the previous volumes are still here: free probability, rough paths, limit theorems for general processes (here fractional Brownian motion and polymers), and large deviations.Lastly, this volume explores new topics, including variable length Markov chains and peacocks. We hope that the whole volume is a good sample of the main streams of current research on probability and stochastic processes, in particular those active in France.

The 39th volume of Seminaire de Probabilites is a tribute to the memory of Paul Andre Meyer. His life and achievements are recalled; homages are rendered by his friends and colleagues. This volume also contains mathematical contributions to classical and quantum stochastic calculus, the theory of processes, martingales and their applications to mathematical finance, Brownian motion. They provide an overview on the current trends of stochastic calculus.

Stochastic processes are as usual the main subject of the Seminaire, with contributions on Brownian motion (fractional or other), Levy processes, martingales and probabilistic finance. Other probabilistic themes are also present: large random matrices, statistical mechanics. The contributions in this volume provide a sampling of recent results on these topics. All contributions with the exception of two are written in English language.

The series of advanced courses initiated in Seminaire de Probabilites XXXIII continues with a course by Ivan Nourdin on Gaussian approximations using Malliavin calculus. The Seminaire also occasionally publishes a series of contributions on a unifying subject; in this spirit, selected participants to the September 2011 Conference on Stochastic Filtrations, held in Strasbourg and organized by Michel Emery, have also contributed to the present volume. The rest of the work covers a wide range of topics, such as stochastic calculus and Markov processes, random matrices and free probability, and combinatorial optimization.

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, Besancon, 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.

This volume represents a part of the main result obtained bya group of French probabilists, together with thecontributions of a number of colleagues, mainly from the USAand Japan. All the papers present new results obtained during theacademic year 1991-1992. The main themes of the papers are:quantum probability (P.A. Meyer and S. Attal), stochasticcalculus (M. Nagasawa, J.B. Walsh, F. Knight, to name a fewauthors), fine properties of Brownian motion (Bertoin,Burdzy, Mountford), stochastic differential geometry(Arnaudon, Elworthy), quasi-sure analysis (Lescot, Song,Hirsch). Taken all together, the papers contained in this volumereflect the main directions of the most up-to-date researchin probability theory. FROM THE CONTENTS: J.P. Ansal, C. Stricker: Unicite etexistence de la loi minimale.- K. Kawazu, H. Tanaka: On themaximum of a diffusion process in a drifted Brownianenvironment.- P.A. Meyer: Representation de martingalesd'operateurs, d'apres Parthasarathy-Sinha.- K. Burdzy:Excursion laws and exceptional points on Brownian paths.- X. Fernique: Convergence en loi de variables aleatoires et defonctions aleatoires, proprietes de compacite des lois, II.-M. Nagasawa: Principle ofsuperposition and interference ofdiffusion processes.- F. Knight: Some remarks on mutualwindings.- S. Song: Inegalites relatives aux processusd'Ornstein-Ulhenbeck a n-parametres et capacite gaussiennec (n,2).- S. Attal, P.A. Meyer: Interpretation probabilisteet extension des integrales stochastiques non commutatives.-J. Azema, Th. Jeulin, F. Knight,M. Yor: Le theoreme d'arreten une fin d'ensemble previsible.

This volume contains 19 contributions to various subjects in the theory of (commutative and non-commutative) stochastic processes. It also provides a 145-page graduate course on branching and interacting particle systems, with applications to non-linear filtering, by P. del Moral and L. Miclo.

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.