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Volume 9, Issue 4
Split-Step Forward Milstein Method for Stochastic Differential Equation

S. Singh

Int. J. Numer. Anal. Mod., 9 (2012), pp. 970-981.

Published online: 2012-09

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  • Abstract

In this paper, we consider the problem of computing numerical solutions for stochastic differential equations (SDEs) of Itô form. A fully explicit method, the split-step forward Milstein (SSFM) method, is constructed for solving SDEs. It is proved that the SSFM method is convergent with strong order $\gamma=1$ in the mean-square sense. The analysis of stability shows that the mean-square stability properties of the method proposed in this paper are an improvement on the mean-square stability properties of the Milstein method and three stage Milstein methods.

  • Keywords

Stochastic differential equation, Explicit method, Mean convergence, Mean square convergence, Stability, Numerical experiment.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-9-970, author = {S. Singh}, title = {Split-Step Forward Milstein Method for Stochastic Differential Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2012}, volume = {9}, number = {4}, pages = {970--981}, abstract = {

In this paper, we consider the problem of computing numerical solutions for stochastic differential equations (SDEs) of Itô form. A fully explicit method, the split-step forward Milstein (SSFM) method, is constructed for solving SDEs. It is proved that the SSFM method is convergent with strong order $\gamma=1$ in the mean-square sense. The analysis of stability shows that the mean-square stability properties of the method proposed in this paper are an improvement on the mean-square stability properties of the Milstein method and three stage Milstein methods.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/668.html} }
TY - JOUR T1 - Split-Step Forward Milstein Method for Stochastic Differential Equation AU - S. Singh JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 970 EP - 981 PY - 2012 DA - 2012/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/668.html KW - Stochastic differential equation, Explicit method, Mean convergence, Mean square convergence, Stability, Numerical experiment. AB -

In this paper, we consider the problem of computing numerical solutions for stochastic differential equations (SDEs) of Itô form. A fully explicit method, the split-step forward Milstein (SSFM) method, is constructed for solving SDEs. It is proved that the SSFM method is convergent with strong order $\gamma=1$ in the mean-square sense. The analysis of stability shows that the mean-square stability properties of the method proposed in this paper are an improvement on the mean-square stability properties of the Milstein method and three stage Milstein methods.

S. Singh. (2012). Split-Step Forward Milstein Method for Stochastic Differential Equation. International Journal of Numerical Analysis and Modeling. 9 (4). 970-981. doi:
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