FoCM 2014 conference
Workshop C6 - Stochastic Computation
December 20, 15:30 ~ 16:00 - Room C11
A perturbation formula as universal tool for strong approximations of stochastic differential equations
Martin Hutzenthaler
University of Duisburg-Essen, Germany - martin.hutzenthaler@uni-due.de
The main object of this talk is a pathwise perturbation formula for stochastic differential equations (SDEs) which expresses the distance between the solution and any It\^o process in terms of the distances of the local characteristics. Together with suitable integrability properties, this is a convenient tool for proving strong convergence rates of various approximations of SDEs. For example, this yields a sufficient condition for local Lipschitz continuity in the strong sense in the initial value, a sufficient condition for explicit numerical approximations of finite-dimensional SDEs and a sufficient condition for spatial discretizations of nonlinear SPDEs. We illustrate these conditions with example SDEs from finance, physics and biology.
Joint work with Sonja Cox (University of Amsterdam, Netherlands), Arnulf Jentzen (ETH Zurich, Switzerland) and Xiaojie Wang (Changsha, China).