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

2018/07/24 by Lan, Guangqiang, Wang, Qiushi
#60H10 #65C30 #65L20 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1807.08983

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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