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High order numerical integrators for single integrand Stratonovich SDEs (2004.12887v2)
Published 27 Apr 2020 in math.NA, cs.NA, and math.PR
Abstract: We show that applying any deterministic B-series method of order $p_d$ with a random step size to single integrand SDEs gives a numerical method converging in the mean-square and weak sense with order $\lfloor p_d/2\rfloor$.As an application, we derive high order energy-preserving methods for stochastic Poisson systems as well as further geometric numerical schemes for this wide class of Stratonovich SDEs.