Stepsize control for mean-square numerical methods for stochastic differential equations with small noise

A strategy for controlling the stepsize in the numerical integration of stochastic differential equations (SDEs) is presented. It is based on estimating the p-th mean of local errors. The strategy leads to deterministic stepsize sequences that are identical for all paths. For the family of Euler schemes for SDEs with small noise we derive computable estimates for the dominating term of the p-th mean of local errors and show that the strategy becomes efficient for reasonable stepsizes. Numerical experience is reported for test examples including scalar SDEs and a stochastic circuit model