Bücher der Reihe Seminaire de Probabilites in Reihenfolge

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.

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.

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.

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.

This 49th volume offers a good sample of the main streams of current research on probability and stochastic processes, in particular those active in France. This includes articles on latest developments on diffusion processes, large deviations, martingale theory, quasi-stationary distribution, random matrices, and many more.

La methode des semi-mrtingales en filtrage quand l'observation est un processus ponctuel marque.- One-dimensional potential embedding.- Un theoreme de representation des martingales pour les ensembles regeneratifs.- A simple remark on the conditioned square functions for martingale transforms.- Absolute continuity of Markov processes.- Germ-field Markov property for multiparameter processes.- La theorie de la prediction de F. Knight.- Sur la theorie de la prediction, et le probleme de decomposition des tribus F t+ o .- Generation of ?-fields by step processes.- Les inegalites classiques.- L'operateur carré du champ.- Correction aux "Inegalites de LITTLEWOOD-PALET".- Les inegalites generales.- Semi-groupes de convolution symetriques.- A probabilistic approach to non-linear Dirichlet problem.- Skorokhod stopping times of minimal variance.- On the krickeberg decomposition of continuous martingales.- The Q-matrix problem.- On a stopped Brownian motion formula of H.M. Taylor.- On the uniqueness of solutions of stochastic differential equations with reflecting barrier conditions.- et notations generales.- Chapitre I. Integrales de stieltjes stochastiques.- Chapitre II. Martingales de carré integrable.- Chapitre III: La formule du changement de variables forme préliminaire.- Martingales locales changement de variables, formules exponentielles.- Les espaces H 1 et BMO.- Complements aux chapitres I-V.- Sur certains espaces de martingales localement de carre integrable.- Espaces fortement stables de martingales de carre integrable.- Representation des martingales comme integrales stochastiques des processus optionnels.- Decompositions des martingales locales et formules exponentielles.- Sur les integrales stochastiques optionnelles et une suite remarquable de formules exponentielles.- Sur la decomposition multiplicative des sousmartingales positives.- The Q-matrix problem 2: KOLMOGOROV backward equations.- Separabilite optionnelle, d'apres doob.- Note on pasting of two Markov processes.- A characterization of BMO-martingales.- Demonstration elementaire d'un theoreme de Novikov.- Corrections a des exposes de 1973/74.- Sur la construction de noyaux boreliens.- Un point de priorite.- Complements aux exposes sur les ensembles analytiques et les temps d'Arret.

This milestone 50th volume of the "Seminaire de Probabilites" pays tribute with a series of memorial texts to one of its former editors, Jacques Azema, who passed away in January.