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Conservative methods for stochastic differential equations with a conserved quantity
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.ORCID iD: 0000-0001-6490-1957
2016 (English)In: International Journal of Numerical Analysis and Modeling, ISSN 1923-2942, Vol. 13, no 3, 435-456 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2016. Vol. 13, no 3, 435-456 p.
Keyword [en]
stochastic differential equations, invariants, conservative methods, stochastic geometric numerical integration, quadrature formula, splitting technique, mean-square convergence order, weak convergence order
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-99206OAI: oai:DiVA.org:umu-99206DiVA: diva2:786095
Available from: 2015-02-04 Created: 2015-02-04 Last updated: 2017-12-05Bibliographically approved

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