Séminaire de Probabilités XLIV, 2012 Séminaire de Probabilités Series

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.

Context trees, variable length Markov chains and dynamical sources.- Martingale property of generalized stochastic exponentials.- Some classes of proper integrals and generalized Ornstein-Uhlenbeck processes.- Martingale representations for diffusion processes and backward stochastic differential equations.- Quadratic Semimartingale BSDEs Under an Exponential Moments Condition.- The derivative of the intersection local time of Brownian motion through Wiener chaos.- On the occupation times of Brownian excursions and Brownian loops.- Discrete approximation to solution flows of Tanaka’s SDE related to Walsh Brownian motion.- Spectral Distribution of the Free unitary Brownian motion: another approach.- Another failure in the analogy between Gaussian and semicircle laws.- Global solutions to rough differential equations with unbounded vector fields.- Asymptotic behavior of oscillatory fractional processes.- Time inversion property for rotation invariant self-similar diffusion processes.- On Peacocks: a general introduction to two articles.- Some examples of peacocks in a Markovian set-up.- Peacocks obtained by normalisation; strong and very strong peacocks.- Branching Brownian motion: Almost sure growth along scaled paths.- On the delocalized phase of the random pinning model.- Large deviations for Gaussian stationary processes and semi-classical analysis.- Girsanov theory under a finite entropy condition.

This volume provides a broad insights on current, high level researches in probability theory Includes supplementary material: sn.pub/extras