Séminaire de Probabilités XXXV (English and French Edition)

Researchers and graduate students in the theory of stochastic processes will find in this 35th volume some thirty articles on martingale theory, martingales and finance, analytical inequalities and semigroups, stochastic differential equations, functionals of Brownian motion and of Lévy processes. Ledoux's article contains a self-contained introduction to the use of semigroups in spectral gaps and logarithmic Sobolev inequalities; the contribution by Emery and Schachermayer includes an exposition for probabilists of Vershik's theory of backward discrete filtrations. This volume contains 30 articles on martingale theory, martingales and finance, analytical inequalities and semigroups, stochastic differential equations, functionals of Brownian motion and of Levy processes. The Brownian and Poisson processes can be realized as operator processes on the symmetric Fock space, the classical notion of independence of increments being expressed in Fock space using tensor products.