This milestone 50 th volume of the "Séminaire de Probabilités" pays tribute with a series of memorial texts to one of its former editors, Jacques Azéma, who passed away in January. The founders of the "Séminaire de Strasbourg", which included Jacques Azéma, probably had no idea of the possible longevity and success of the process they initiated in 1967. Continuing in this long tradition, this volume contains contributions on state-of-art research on Brownian filtrations, stochastic differential equations and their applications, regularity structures, quantum diffusion, interlacing diffusions, mod-Ø convergence, Markov soup, stochastic billiards and other current streams of research.

Features contributions on state-of-the-art research in probability Covers mainstream domains Includes accessible presentations of classical results

Inhalt

• Part I In memoriam Jacques Azéma. - Un témoignage. - Un dimanche de juin avec Jacques. - Mosaïque de Poisson-Voronoi sur une surface. - Sur le retournement du temps. - La martingale d'Azéma. - Part II Regular Contributions. - Complementability and Maximality in Different Contexts: Ergodic Theory, Brownian and Poly-Adic Filtrations. - Uniform Entropy Scalings of Filtrations. - Solving Rough Differential Equations with the Theory of Regularity Structures. - On the EulerMaruyama Scheme for Degenerate Stochastic Differential Equations with Non-sticky Condition. - On a Construction of Strong Solutions for Stochastic Differential Equations with Non-Lipschitz Coefficients: A Priori Estimates Approach. - Heat Kernel Coupled with Geometric Flow and Ricci Flow. - Scaled Penalization of Brownian Motion with Drift and the Brownian Ascent. - Interlacing Diffusions. - Brownian Sheet Indexed by RN: Local Time and Bubbles. - Mod- Convergence, II: Estimates on the Speed of Convergence. - Random Flows Defined by Markov Loops. - Brownian Winding Fields. - Recurrence and Transience of Continuous-Time Open Quantum Walks. - Explicit Speed of Convergence of the Stochastic Billiard in a Convex Set.