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This is a new volume of the Séminaire de Probabilité which was started in the 60's. Following the tradition, this volume contains up to 20 original research and survey articles on several topics related to stochastic analysisThis volume contains J. Picard's advanced course on the representation formulae for the fractional Brownian motion. The regular chapters
cover a wide range of themes, such as stochastic calculus and stochastic differential
equations, stochastic differential geometry, filtrations, analysis of Wiener space, random matrices and free probability, as well as mathematical finance. Some of the contributions were presented at the Journées de Probabilités held in Poitiers in June 2009.