Catherine Donati-Martin - Böcker

This milestone 50th 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.

This volume presents a selection of texts that reflects the current research streams in probability, with an interest toward topics such as filtrations, Markov processes and Markov chains as well as  large deviations, Stochastic Partial Differential equations, rough paths theory, quantum probabilities and percolation on graphs.The featured contributors are R. L. Karandikar and B. V. Rao,  C. Leuridan,  M. Vidmar, L. Miclo and P. Patie,  A. Bernou,  M.-E. Caballero and A. Rouault,  J. Dedecker, F. Merlevède and E. Rio, F. Brosset, T. Klein, A. Lagnoux and P. Petit,  C. Marinelli and L. Scarpa,  C. Castaing, N. Marie and P. Raynaud de Fitte,  S. Attal, J. Deschamps and C. Pellegrini,  and N. Eisenbaum.

This volume closes the Séminaire de Probabilités, a long and rich series that started in 1966 under the name Séminaire de Probabilités de Strasbourg.

The series of advanced courses initiated in Séminaire de Probabilités XXXIII continues with a course by Ivan Nourdin on Gaussian approximations using Malliavin calculus. The Séminaire also occasionally publishes a series of contributions on a unifying subject; in this spirit, selected participants to the September 2011 Conference on Stochastic Filtrations, held in Strasbourg and organized by Michel Émery, have also contributed to the present volume. The rest of the work covers a wide range of topics, such as stochastic calculus and Markov processes, random matrices and free probability, and combinatorial optimization.

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.

This volume is dedicated to the memory of Marc Yor, who passed away in 2014. The invited contributions by his collaborators and former students bear testament to the value and diversity of his work and of his research focus, which covered broad areas of probability theory. The volume also provides personal recollections about him, and an article on his essential role concerning the Doeblin documents.With contributions by P. Salminen, J-Y. Yen & M. Yor; J. Warren; T. Funaki; J. Pitman& W. Tang; J-F. Le Gall; L. Alili, P. Graczyk & T. Zak; K. Yano & Y. Yano; D. Bakry & O. Zribi; A. Aksamit, T. Choulli & M. Jeanblanc; J. Pitman; J. Obloj, P. Spoida & N. Touzi; P. Biane; J. Najnudel; P. Fitzsimmons, Y. Le Jan & J. Rosen; L.C.G. Rogers & M. Duembgen; E. Azmoodeh, G. Peccati & G. Poly, timP-L Méliot, A. Nikeghbali; P. Baldi; N. Demni, A. Rouault & M. Zani; N. O'Connell; N. Ikeda & H. Matsumoto; A. Comtet & Y. Tourigny; P. Bougerol; L. Chaumont; L. Devroye & G. Letac; D. Stroock and M. Emery.

In addition to its further exploration of the subject of peacocks, introduced in recent Séminaires de Probabilités, this volume continues the series’ focus on current research themes in traditional topics such as stochastic calculus, filtrations and random matrices.

This 49th volume offers a good sample of the main streams of current research on probability and stochastic processes, in particular those active in France. This includes articles on latest developments on diffusion processes, large deviations, martingale theory, quasi-stationary distribution, random matrices, and many more.

Two noteworthy features of the 40th volume of Seminaire de Probabilites are L. Coutin's advanced course on calculus driven by fractional Brownian motion, and a series of seven interrelated works on local time-space calculus. Other topics from stochastic processes and stochastic finance include three contributions by A.S. Cherny on general approaches to arbitrage pricing.

Stochastic processes are as usual the main subject of the Séminaire, with contributions on Brownian motion (fractional or other), Lévy processes, martingales and probabilistic finance. Other probabilistic themes are also present: large random matrices, statistical mechanics. The contributions in this volume provide a sampling of recent results on these topics. All contributions with the exception of two are written in English language.

Nine volumes ago, in S' eminaire de Probabilit' es XXXIII, a series of advanced courses was started; nine such courses have appeared since. Two of them are due to Antoine Lejay, including his Introduction to rough paths in v- umeXXXVII. Thisunrepentantrecidivistnowstrikesagain,withYetanother introduction to rough paths, which sheds a more algebraic light on the same matter. The various contributions which constitute the rest of the volume ex- plify the r ole the S' eminaire intends to play on the probabilistic stage: junior authors go side by side with older contributors, with a predominance from French or francophile ones; short notes mix with real research articles; and the themes are well in the traditional spirit of the S' eminaire, ranging over the broad spectrum of interest of the readership of the S' eminaire. ' Catherine Donati-Martin, Michel Emery, Alain Rouault, Christophe Stricker vii Contents Yet Another Introduction to Rough Paths Antoine Lejay...1 Monotonicity of the Extremal Functions for One-dimensional Inequalities of Logarithmic Sobolev Type Laurent Miclo...103 Non-monotone Convergence in the Quadratic Wasserstein Distance Walter Schachermayer, Uwe Schmock, and Josef Teichmann...131 On the Equation ? =S ??? t t Fangjun Xu...137 Shabat Polynomials and Harmonic Measure Philippe Biane...147 Radial Dunkl Processes Associated with Dihedral Systems Nizar Demni...153 Matrix Valued Brownian Motion and a Paper by P' olya Philippe Biane...171 On the Laws of First Hitting Times of Points for One-dimensional Symmetric Stable L' evy Processes Kouji Yano, Yuko Yano, and Marc Yor...

This is a new volume of the Séminaire de Probabilités which is now in its 43rd year. Following the tradition, this volume contains about 20 original research and survey articles on topics related to stochastic analysis. It contains an advanced course of J. Picard on the representation formulae for fractional Brownian motion. The regular chapters cover a wide range of themes, such as stochastic calculus and stochastic differentialequations, stochastic differential geometry, filtrations, analysis on 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.