Conservative Methods for Stochastic Differential Equations with a Conserved Quantity

Conservative Methods for Stochastic Differential Equations with a Conserved Quantity

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.