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Besides topics traditionally found in the Séminaire de Probabilités (Martingale Theory, Stochastic Processes, questions of general interest in Probability Theory), this volume XXXIII presents nine contributions to the study of filtrations up to isomorphism. It also contains three graduate courses: Dynamics of stochastic algorithms, by M. Benaim; Simulated annealing algorithms and Markov chains with rare transitions, by O. Catoni; and Concentration of measure and logarithmic Sobolev inequalities, by M. Ledoux. These up to date courses present the state of the art in three matters of interest to students in theoretical or applied Probability Theory, and to researchers as well.
List of contents
Dynamics of stochastic approximation algorithms.- Simulated annealing algorithms and Markov chains with rare transitions / Algorithmes de recuit simulé et chaînes de Markov à transitions rares.- Concentration of measure and logarithmic Sobolev inequalities.- Une simplification de l'argument de Tsirelson sur le caractere non-brownien des processus de walsh.- On certain probabilities equivalent to Wiener measure, d'Après Dubins, Feldman, Smorodinsky and Tsirelson.- On certain probabilities equivalent to Coin-Tossing, d'Après Schachermayer.- On the joining of sticky brownian motion.- Brownian filtrations are not stable under equivalent time-changes.- The existence of a multiple spider martingale in the natural filtration of a certain diffusion in the plane.- A remark on Tsirelson's stochastic differential equation.- Appendice à l'exposé précédent: La filtration naturelle du mouvement brownien indexé par ? dans une variété compacte.- A stochastic differential equation with a unique (up to indistinguishability) but not strong solution.- Some remarks on the uniform integrability of continuous martingales.- An alternative proof of a theorem of Aldous concerning convergence in distribution for martingales.- A short proof of decomposition of strongly reduced martingales.- Some remarks on L?, H? and BMO.- A bipolar theorem for .- Barycentre canonique pour un espace métrique à courbure négative.- Dualité du problème des marges et ses applications.- The distribution of local times of a Brownian bridge.- Paths of finitely additive Brownian Motion need not be bizarre.- A limit theorem for the prediction process under absolute continuity.- Processus gouvernés par des noyaux.- Sur l'hypercontractivite des semi-groupes ultraspheriques.- An addendum to aremark on Slutsky's theorem.- Theoremes limites pour les temps locaux d'un processus stable symetrique.
