Year: 2016
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 3 : pp. 435–456
Abstract
This paper proposes a novel conservative method for the numerical approximation of general stochastic differential equations in the Stratonovich sense with a conserved quantity. We show that the mean-square order of the method is 1 if noises are commutative and that the weak order is 1 in the general case. Since the proposed method may need the computation of a deterministic integral, we analyse the effect of the use of quadrature formulas on the convergence orders. Furthermore, based on the splitting technique of stochastic vector fields, we construct conservative composition methods with similar orders as the above method. Finally, numerical experiments are presented to support our theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-IJNAM-447
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 3 : pp. 435–456
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Stochastic differential equations invariants conservative methods stochastic geometric numerical integration quadrature formula splitting technique mean-square convergence order weak convergence order.