Ebook: Stochastic Analysis and Related Topics: In Honour of Ali Süleyman Üstünel, Paris, June 2010

Since the early eighties, Ali Süleyman Üstünel has been one of the main contributors to the field of Malliavin calculus. In a workshop held in Paris, June 2010 several prominent researchers gave exciting talks in honor of his 60^th birthday. The present volume includes scientific contributions from this workshop.
Probability theory is first and foremost aimed at solving real-life problems containing randomness. Markov processes are one of the key tools for modeling that plays a vital part concerning such problems. Contributions on inventory control, mutation-selection in genetics and public-private partnerships illustrate several applications in this volume. Stochastic differential equations, be they partial or ordinary, also play a key role in stochastic modeling. Two of the contributions analyze examples that share a focus on probabilistic tools, namely stochastic analysis and stochastic calculus. Three other papers are devoted more to the theoretical development of these aspects. The volume addresses graduate students and researchers interested in stochastic analysis and its applications.

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Random matrix theory is an area of mathematics first developed by physicists interested in the energy levels of atomic nuclei, but it can also be used to describe some exotic phenomena in the number theory of elliptic curves. This book illustrates this interplay of number theory and random matrices. It begins with an introduction to elliptic curves and the fundamentals of modeling by a family of random matrices, and moves on to highlight the latest research. There are expositions of current research on ranks of elliptic curves, statistical properties of families of elliptic curves and their associated L-functions and the emerging uses of random matrix theory in this field. Most of the material here had its origin in a Clay Mathematics Institute workshop on this topic at the Newton Institute in Cambridge and together these contributions provide a unique in-depth treatment of the subject 1.Boubacar Bah, Etienne Pardoux and Ahmadou Bamba Sow: A look-down model with selection.- 2.Alain Bensoussan: Control of Inventories with Markov Demand.- 3.Zdzislaw Brzezniak and Annie Millet: On the splitting method for some complex-valued quasilinear evolution equations.- 4. Caroline Hillairet and Monique Pontier: A Modelisation of Public Private Parternships with failure time.- 5.Joseph Najnudel, Daniel Stroock and Marc Yor: On a flow of transformations of a Wiener space.- 6.Nicolas Privault: Measure invariance on the Lie-Wiener path space.- 7.Denis Talay: Derivatives of Solutions of Semilinear Parabolic PDEs and Variational Inequalities with Neumann Boundary Conditions.- 8.Samy Tindel and Ivan Torrecilla: Some differential systems driven by a fBm with Hurst parameter greater than ...- 9.Ali Suleyman Ustunel: Transportation cost inequalities for diffusions under uniform distance.- Glossary. ai