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arXiv · 1610.04003

Adaptive timestepping strategies for nonlinear stochastic systems

Cónall Kelly·Gabriel J. Lord
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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.

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Cónall Kelly, Gabriel J. Lord. 2016-10-13. Adaptive timestepping strategies for nonlinear stochastic systems. https://arxiv.org/abs/1610.04003

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