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Volume 13, Issue 3
Conservative Methods for Stochastic Differential Equations with a Conserved Quantity

C.-C. Chen, D. Cohen & J.-L. Hong

Int. J. Numer. Anal. Mod., 13 (2016), pp. 435-456.

Published online: 2016-05

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  • 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.

  • Keywords

Stochastic differential equations, invariants, conservative methods, stochastic geometric numerical integration, quadrature formula, splitting technique, mean-square convergence order, weak convergence order.

  • AMS Subject Headings

60H10, 60H35, 65C20, 65C30, 65D30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-435, author = {}, title = {Conservative Methods for Stochastic Differential Equations with a Conserved Quantity}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {3}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/447.html} }
TY - JOUR T1 - Conservative Methods for Stochastic Differential Equations with a Conserved Quantity JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 435 EP - 456 PY - 2016 DA - 2016/05 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/447.html KW - Stochastic differential equations, invariants, conservative methods, stochastic geometric numerical integration, quadrature formula, splitting technique, mean-square convergence order, weak convergence order. AB -

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.

C.-C. Chen, D. Cohen & J.-L. Hong. (1970). Conservative Methods for Stochastic Differential Equations with a Conserved Quantity. International Journal of Numerical Analysis and Modeling. 13 (3). 435-456. doi:
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