Simulating systems of Itô SDEs with split-step $ (\alpha, \beta) $-Milstein scheme

In the present study, we provide a new approximation scheme for solving stochastic differential equations based on the explicit Milstein scheme. Under sufficient conditions, we prove that the split-step $ (\alpha, \beta) $-Milstein scheme strongly convergence to the exact solution with order $ 1.0 $...

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Bibliographic Details
Published inAIMS mathematics Vol. 8; no. 2; pp. 2576 - 2590
Main Authors Ranjbar, Hassan, Torkzadeh, Leila, Baleanu, Dumitru, Nouri, Kazem
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
itô stochastic ordinary differential equations
mean-square convergence
mean-square stability
split-step milstein scheme
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ISSN2473-6988
2473-6988
DOI10.3934/math.2023133

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Summary:In the present study, we provide a new approximation scheme for solving stochastic differential equations based on the explicit Milstein scheme. Under sufficient conditions, we prove that the split-step $ (\alpha, \beta) $-Milstein scheme strongly convergence to the exact solution with order $ 1.0 $ in mean-square sense. The mean-square stability of our scheme for a linear stochastic differential equation with single and multiplicative commutative noise terms is studied. Stability analysis shows that the mean-square stability of our proposed scheme contains the mean-square stability region of the linear scalar test equation for suitable values of parameters $ \alpha, \beta $. Finally, numerical examples illustrate the effectiveness of the theoretical results.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2023133