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Volume 5, Issue 4
Convergence Analysis of a Splitting Method for Stochastic Differential Equations

W. Zhao, L. Tian & L. Ju

Int. J. Numer. Anal. Mod., 5 (2008), pp. 673-692.

Published online: 2008-05

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  • Abstract

In this paper, we propose a fully drift-implicit splitting numerical scheme for the stochastic differential equations driven by the standard $d$-dimensional Brownian motion. We prove that its strong convergence rate is of the same order as the standard Euler-Maruyama method. Some numerical experiments are also carried out to demonstrate this property. This scheme allows us to use the latest information inside each iteration in the Euler-Maruyama method so that better approximate solutions could be obtained than the standard approach.

  • Keywords

stochastic differential equation, drift-implicit splitting scheme, Brownian motion.

  • AMS Subject Headings

65C20, 65C30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-5-673, author = {W. Zhao, L. Tian and L. Ju}, title = {Convergence Analysis of a Splitting Method for Stochastic Differential Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2008}, volume = {5}, number = {4}, pages = {673--692}, abstract = {

In this paper, we propose a fully drift-implicit splitting numerical scheme for the stochastic differential equations driven by the standard $d$-dimensional Brownian motion. We prove that its strong convergence rate is of the same order as the standard Euler-Maruyama method. Some numerical experiments are also carried out to demonstrate this property. This scheme allows us to use the latest information inside each iteration in the Euler-Maruyama method so that better approximate solutions could be obtained than the standard approach.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/832.html} }
TY - JOUR T1 - Convergence Analysis of a Splitting Method for Stochastic Differential Equations AU - W. Zhao, L. Tian & L. Ju JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 673 EP - 692 PY - 2008 DA - 2008/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/832.html KW - stochastic differential equation, drift-implicit splitting scheme, Brownian motion. AB -

In this paper, we propose a fully drift-implicit splitting numerical scheme for the stochastic differential equations driven by the standard $d$-dimensional Brownian motion. We prove that its strong convergence rate is of the same order as the standard Euler-Maruyama method. Some numerical experiments are also carried out to demonstrate this property. This scheme allows us to use the latest information inside each iteration in the Euler-Maruyama method so that better approximate solutions could be obtained than the standard approach.

W. Zhao, L. Tian and L. Ju. (2008). Convergence Analysis of a Splitting Method for Stochastic Differential Equations. International Journal of Numerical Analysis and Modeling. 5 (4). 673-692. doi:
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