Volume 17, Issue 5
Modifying the Split-Step $θ$-Method with Harmonic-Mean Term for Stochastic Differential Equations

Int. J. Numer. Anal. Mod., 17 (2020), pp. 662-678.

Published online: 2020-08

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• Abstract

In this paper, we design a class of general split-step methods for solving Itô stochastic differential systems, in which the drift or deterministic increment function can be taken from special ordinary differential equations solver, based on the harmonic-mean. This method is justified to have a strong convergence order of $\frac{1}{2}$. Further, we investigate mean-square stability of the proposed method for linear scalar stochastic differential equation. Finally, some examples are included to demonstrate the validity and efficiency of the introduced scheme.

• Keywords

Itô stochastic differential system, split-step method, ODE solver, harmonic-mean, strong convergence, mean-square stability.

• AMS Subject Headings

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@Article{IJNAM-17-662, author = {Nouri , Kazem and Ranjbar , Hassan and Carlos Cortés López , Juan}, title = {Modifying the Split-Step $θ$-Method with Harmonic-Mean Term for Stochastic Differential Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {5}, pages = {662--678}, abstract = {

In this paper, we design a class of general split-step methods for solving Itô stochastic differential systems, in which the drift or deterministic increment function can be taken from special ordinary differential equations solver, based on the harmonic-mean. This method is justified to have a strong convergence order of $\frac{1}{2}$. Further, we investigate mean-square stability of the proposed method for linear scalar stochastic differential equation. Finally, some examples are included to demonstrate the validity and efficiency of the introduced scheme.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/17874.html} }
TY - JOUR T1 - Modifying the Split-Step $θ$-Method with Harmonic-Mean Term for Stochastic Differential Equations AU - Nouri , Kazem AU - Ranjbar , Hassan AU - Carlos Cortés López , Juan JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 662 EP - 678 PY - 2020 DA - 2020/08 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/17874.html KW - Itô stochastic differential system, split-step method, ODE solver, harmonic-mean, strong convergence, mean-square stability. AB -

In this paper, we design a class of general split-step methods for solving Itô stochastic differential systems, in which the drift or deterministic increment function can be taken from special ordinary differential equations solver, based on the harmonic-mean. This method is justified to have a strong convergence order of $\frac{1}{2}$. Further, we investigate mean-square stability of the proposed method for linear scalar stochastic differential equation. Finally, some examples are included to demonstrate the validity and efficiency of the introduced scheme.

Kazem Nouri, Hassan Ranjbar & Juan Carlos Cortés López. (2020). Modifying the Split-Step $θ$-Method with Harmonic-Mean Term for Stochastic Differential Equations. International Journal of Numerical Analysis and Modeling. 17 (5). 662-678. doi:
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