An explicit split-step truncated Milstein method for stochastic differential equations

Haghighi, Amir

doi:10.22034/cmde.2022.51249.2132

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	An explicit split-step truncated Milstein method for stochastic differential equations
Computational Methods for Differential Equations
مقاله 2، دوره 11، شماره 4، مهر 2023، صفحه 676-695 اصل مقاله (424.91 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.51249.2132
نویسنده
Amir Haghighi^*
Department of Mathematics, Faculty of Science, Razi University, Kermanshah 67149, Iran.
چکیده
In this paper, we propose an explicit split-step truncated Milstein method for stochastic differential equations (SDEs) with commutative noise. We discuss the mean-square convergence properties of the new method for numerical solutions of a class of highly nonlinear SDEs in a finite time interval. As a result, we show that the strong convergence rate of the new method can be arbitrarily close to one under some additional conditions. Finally, we use an illustrative example to highlight the advantages of our new findings in terms of both stability and accuracy compared to the results in Guo et al. (2018).
کلیدواژه‌ها
Stochastic differential equations؛ Non-globally Lipschitz conditions؛ strong convergence rate؛ Truncated Milstein method؛ Split-step methods

مراجع
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An explicit split-step truncated Milstein method for stochastic differential equations