Adaptive timestepping strategies for nonlinear stochastic systems

Conall Kelly, Gabriel James Lord

Research output: Contribution to journalArticle

10 Citations (Scopus)
30 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)1523–1549
Number of pages27
JournalIMA Journal of Numerical Analysis
Volume38
Issue number3
DOIs
Publication statusPublished - 21 Aug 2017

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