Adaptive timestepping strategies for nonlinear stochastic systems
Numerical Analysis
2016-10-14 v1 Probability
Abstract
We introduce a class of adaptive timestepping strategies for stochastic differential equations with non-Lipschitz drift coefficients. These strategies work by controlling potential unbounded growth in solutions of a numerical scheme due to the drift. We prove that the Euler-Maruyama scheme with an adaptive timestepping strategy in this class is strongly convergent. Specific strategies falling into this class are presented and demonstrated on a selection of numerical test problems. We observe that this approach is broadly applicable, can provide more dynamically accurate solutions than a drift-tamed scheme with fixed stepsize, and can improve MLMC simulations.
Cite
@article{arxiv.1610.04003,
title = {Adaptive timestepping strategies for nonlinear stochastic systems},
author = {Cónall Kelly and Gabriel J. Lord},
journal= {arXiv preprint arXiv:1610.04003},
year = {2016}
}