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arXiv · 2008.08249

The Strong Convergence and Stability of Explicit Approximations for Nonlinear Stochastic Delay Differential Equations

Guoting Song·Junhao Hu·Shuaibin Gao·Xiaoyue Li
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Abstract

This paper focuses on explicit approximations for nonlinear stochastic delay differential equations (SDDEs). Under the weakly local Lipschitz and some suitable conditions, a generic truncated Euler-Maruyama (TEM) scheme for SDDEs is proposed, which numerical solutions are bounded and converge to the exact solutions in qth moment for q>0. Furthermore, the 1/2 order convergent rate is yielded. Under the Khasminskii-type condition, a more precise TEM scheme is given, which numerical solutions are exponential stable in mean square and P-1. Finally, several numerical experiments are carried out to illustrate our results.

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Guoting Song, Junhao Hu, Shuaibin Gao, Xiaoyue Li. 2020-08-19. The Strong Convergence and Stability of Explicit Approximations for Nonlinear Stochastic Delay Differential Equations. https://arxiv.org/abs/2008.08249

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