An adaptive timestepping algorithm for stochastic differential equations

Abstract

We introduce a variable timestepping procedure using local error control for the pathwise (strong) numerical integration of a system of stochastic differential equations forced by a single Wiener process. The Milstein method is used to advance the numerical solution and the stepsizes are determined via two local error estimates that roughly correspond to leading order deterministic and stochastic local error components. One advantage of using two error controls is an increased flexibility that allows for the treatment of both drift and diffusion dominated regimes in a consistent manner. Numerical results are presented and the generalization of this approach to wider classes of problems and methods is discussed.