Epsilon-Strong Simulation for Multidimensional Stochastic Differential Equations via Rough Path Analysis

Abstract: Consider a multidimensional diffusion process, X. Let epsilon>0 be a deterministic user defined tolerance error parameter. We develop a systematic way to construct a probability space, supporting both X and a fully simulatable piecewise constant process X_epsilon, such that X_epsilon is within epsilon distance from X under the uniform metric on compact time intervals with probability one. Our construction requires a detailed study of continuity estimates of the Ito map using Lyons' theory of rough paths. We approximate the underlying Brownian paths, jointly with the Levy areas, with a deterministic error bound in the underlying rough path metric.

BIO: Jing Dong is an assistant Professor in the Department of Industrial Engineering and Management Science at Northwestern University. Her research interests are in applied probability, stochastic simulation and stochastic modeling with applications in service operations management. She obtained her Phd in Operations Research from Columbia University. Prior to that she received her BSc in Actuarial Science from Hong Kong University.