Strong convergence rates of modified truncated EM methods for neutral stochastic differential delay equations. (English) Zbl 1418.60059
Summary: 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.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
Keywords:
neutral stochastic differential delay equations; local Lipschitz condition; modified truncated Euler-Maruyama method; strong convergence rateReferences:
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