Gabriel J. Lord est Professeur à l'université Heriot Watt a Edinburgh dans le département de Mathématiques du Maxwell Institute.
Title : Adaptative stepping for SPDEs with non-Lipschitz drift.
Abstract : Traditional explicit numerical methods to simulate SDEs or SPDE) rely on globally Lipschitz drift and diffusion coefficients to ensure convergence. However, many applications of interest include non Lipschitz drift functions. Implicit methods are generally too computationally expensive for practical use. Tamed methods are a class of numerical methods that perturb the drift coefficient to ensure strong convergence in the presence of non-Lipschitz drift. The adaptive time-stepping explicit method we present is an efficient alternative to taming which guarantees strong convergence in the presence of one-sided Lipschitz drift. We highlight the steps in the proof and present numerical experiments that highlight some of the issues involved.