The Improved Stability Analysis of Numerical Method for Stochastic Delay Differential Equations

Yu Zhang, Enying Zhang () and Longsuo Li
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Yu Zhang: School of Economics, Harbin University of Commerce, Harbin 150028, China
Enying Zhang: School of Economics, Harbin University of Commerce, Harbin 150028, China
Longsuo Li: School of Management, Harbin Institute of Technology, Harbin 150001, China

Mathematics, 2022, vol. 10, issue 18, 1-7

Abstract: In this paper, the improved split-step θ method, named the split-step composite θ method, is proposed to study the mean-square stability for stochastic differential equations with a fixed time delay. Under the global Lipschitz and linear growth conditions, it is proved that the split-step composite θ method with θ ≥ 0.5 shows mean-square stability. An approach to improving numerical stability is illustrated by choices of parameters of this method. Some numerical examples are presented to show the accordance between the theoretical and numerical results.

Keywords: stochastic delay differential equations; mean-square stability; split-step composite ? method; split-step ? method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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