Séminaire de Probabilités XXXVII

The 37th Séminaire de Probabilités contains A. Lejay's advanced course which is a pedagogical introduction to works by T. Lyons and others on stochastic integrals and SDEs driven by deterministic rough paths. The rest of the volume consists of various articles on topics familiar to regular readers of the Séminaires, including Brownian motion, random environment or scenery, PDEs and SDEs, random matrices and financial random processes.

Contenu

Preface.- F.B. Knight: An Impression of P.A. Meyer as Deus Ex Machina.- Advanced course: A. Lejay: An introduction to rough paths.- Talks: D. Bakry, O. Mazet : Characterization of Markov semigroups on R associated to some families of orthogonal polynomials.- P. Cheridito: Representations of Gaussian measures that are equivalent to Wiener measure.- L. Galtchouk: On the reduction of a multidimensional continuous martingale to a Brownian motion.- I. Meilijson: The time to a given drawdown in Brownian motion.- A. Lachal: Application de la théorie des excursions à l'intégrale du mouvement Brownien.- T. Mountford: Brownian sheet local time and bubbles.- K. Hirano: On the maximum of a diffusion process in a random Lévy environment.- D. Khoshnevisan: The codimension of the zeros of a stable process in random scenery.- J. Brossard: Deux notions équivalentes d'unicité en loi pour les équations différentielles stochastiques.- Z. Brzezniak, A. Carroll : Approximation of the Wong-Zakai type for stochastic differential equations in M-type 2 Banach spaces with applications to loop spaces.- F. Delarue: Estimates of the solutions of a system of quasi-linear PDEs. A probabilistic scheme.- G. Miermont, J. Schweinsberg: Self-similar fragmentations and stable subordinators.- M. Ledoux: A remark on hypercontractivity and tail inequalities for the largest eigenvalues of random matrices.- Ya. Doumerc: A note on representations of eigenvalues of classical Gaussian matrices.- E. Strasser: Necessary and sufficient conditions for the supermartingale property of a stochastic integral with respect to a local martingale.- M. Rasonyi: A remark on the superhedging theorem under transaction costs.- I. Rosu, D. Stroock: On the derivation of the Black-Scholes formula.- P. del Moral, A. Doucet: On a class of genealogical and interacting Metropolis models.