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Providing a broad overview of the current state of the art in probability theory and its applications, and featuring an article coauthored by Mark Yor, this volume contains contributions on branching processes, Lévy processes, random walks and martingales and their connection with, among other topics, rough paths, semi-groups, heat kernel asymptotics and mathematical finance.

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Sergey Bocharov, Simon C. Harris : Branching random walk in an homogeneous

breeding potential.- A.E. Kyprianou, J.-L. Pérez and Y.X. Ren : The backbone decomposition for spatially dependent supercritical superprocesses.- Lucian Beznea, Iulian Cimpean: On Bochner-Kolmogorov theorem.- Jacques Franchi : Small Time Asymptotics for an Example of Strictly Hypoelliptic Heat Kernel.- Koléhè A. Coulibaly-Pasquier :Onsager-Machlupn functional for uniformly elliptic

time-inhomogeneous diffusion.- Xi Geng, Zhongmin Qian and Danyu Yang : G-Brownian Motion as Rough Paths and Differential Equations Driven by G-Brownian Motion.- Isma el Bailleul : Flows driven by Banach space-valued rough paths.- Christian Léonard : Some properties of path measures.- Patrick Cattiaux, Arnaud Guillin : Semi Log-Concave Markov Diffusions.- Carlo Marinelli,Michael Röckner : On maximal inequalities for purely discontinuous martingales in infinite dimensions.- Walter Schachermayer : Admissible Trading Strategies under Transaction Costs.- A.E. Kyprianou, A.R. Watson: Potentials of stable processes.- Julien Letemplier,Thomas Simon : Unimodality of hitting times for stable processes.- Mathieu Rosenbaum and Marc Yor : On the law of a triplet associated with the pseudo-Brownian bridge.- Jean Brossard, Michel Emery and Christophe Leuridan :Skew-product decomposition of planar Brownian motion and complementability.- Vilmos Prokaj; On the exactness of the Lévy-transformation.- Yinshan Chang : Multi-occupation field generates the Borel-sigma-field of loops.- Ramon van Handel: Ergodicity, Decisions, and Partial Information.- Laurent Serlet : Invariance principle for the random walk conditioned to have a few zeroes.- Dario Trevisian : A short proof of Stein´s universal multiplier theorem.- Joseph Najnudel, Ashkan Nikeghbali : On a flow of operators associated to virtual permutations.

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