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

Kazem Nouri, Hassan Ranjbar & Juan Carlos Cortés López

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.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-17-662, author = {Nouri , KazemRanjbar , 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.

Nouri , KazemRanjbar , Hassan and Carlos Cortés López , Juan. (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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