Strong convergence rates of modified truncated EM methods for neutral stochastic differential delay equations

Guangqiang Lan; Qiushi Wang

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arXiv · 1807.08983

Strong convergence rates of modified truncated EM methods for neutral stochastic differential delay equations

Guangqiang Lan·Qiushi Wang

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Abstract

The aim of this paper is to investigate strong convergence of modified truncated Euler-Maruyama method for neutral stochastic differential delay equations introduced in Lan (2018). Strong convergence rates of the given numerical scheme to the exact solutions at fixed time $T$ are obtained under local Lipschitz and Khasminskii-type conditions. Moreover, convergence rates over a time interval $[0,T]$ are also obtained under additional polynomial growth condition on $g$ without the weak monotonicity condition (which is usually the standard assumption to obtain the convergence rate). Two examples are presented to interpret our conclusions.

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Guangqiang Lan, Qiushi Wang. 2018-07-24. Strong convergence rates of modified truncated EM methods for neutral stochastic differential delay equations. https://arxiv.org/abs/1807.08983

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