Strong Convergence of the Split-Step Theta Method for Stochastic Delay Differential Equations with Nonglobally Lipschitz Continuous Coefficients
Keyword(s):
This paper is concerned with the convergence analysis of numerical methods for stochastic delay differential equations. We consider the split-step theta method for nonlinear nonautonomous equations and prove the strong convergence of the numerical solution under a local Lipschitz condition and a coupled condition on the drift and diffusion coefficients. In particular, these conditions admit that the diffusion coefficient is highly nonlinear. Furthermore, the obtained results are supported by numerical experiments.
2017 ◽
Vol 120
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pp. 215-232
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2017 ◽
Vol 35
(6)
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pp. 766-779
2019 ◽
Vol 17
(06)
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pp. 1950014
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2021 ◽
Vol 382
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pp. 113079
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