14.30-15.15 | Jean Mémin | On the robustness of backward stochastic differential equations |
15.15-16.00 | Harry van Zanten | On Donsker Theorems for Additive Functionals of Ergodic Diffusion Processes |
16.00-16.15 | coffee break | |
16.15-17.00 | Marc Yor | On subordinators, self-similar Markov processes and some factorizations of the exponential variable |
There is ps and a pdf file with program and abstracts
Abstracts |
Jean Mémin: On the robustness of backward stochastic differential
equations In this talk we study the robustness of backward stochastic differential equations (BSDE in short) with respect to the Brownian motion; more precisely we will show that if is a martingale approximation of a Brownian motion then the solution of the BSDE driven by the martingale converges to the solution of the classical BSDE, namely the BSDE driven by . Here we will not assume that has the predictable representation property. As a byproduct of the result we obtain the convergence of the "Euler scheme" for BSDEs corresponding to the case where is a time discretization of . |
Harry van Zanten: On Donsker Theorems for Additive Functionals of Ergodic Diffusion
Processes In this talk we discuss the uniform central limit problem for additive functionals of an ergodic, -dimensional diffusion process. We consider a regular diffusion on an open interval , with finite speed measure and diffusion local time . If is a collection of signed measure on and the total variations of these signed measures are uniformly bounded, we give a sufficient condition on under which the random map converges weakly, as , to a tight weak limit in the space of bounded functions on . The condition on is formulated in terms of the metric entropy of the class with respect to a suitable metric. We also discuss a number of applications of the abstract result. |
Marc Yor: On subordinators, self-similar Markov processes and some factorizations of the
exponential variable In this lecture, I shall prove that if is the `exponential functional' associated to , a subordinator, then it is always a factor in a multiplicative decomposition of the exponential variable. I shall illustrate this result with several examples. |