Strong convergence of the partially truncated Euler-Maruyama method for a class of stochastic differential delay equations
Strong convergence of the partially truncated Euler-Maruyama method for a class of stochastic differential delay equations
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DOI：
10.1016/j.cam.2017.11.030
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发表时间：
2018-06
期刊：
影响因子：
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通讯作者：
Wei Zhang-;M. Song;M. Liu
中科院分区：
文献类型：
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作者：
Wei Zhang-;M. Song;M. Liu
本文建立了一类高度非线性随机时滞微分方程解的收敛性定理，而不需要用Khasminskii型条件代替线性增长条件，因此这里的收敛准则可以覆盖更广泛的一类非线性系统.研究了随机时滞微分方程dy（t）= f（y（t），y（t− τ））dt + g（y（t），y（t − τ））dw（t）的部分截断Euler-Maruyama方法，并在局部Lipschitz条件和Khasminskii-型条件下，考虑了2≤ q< p的强Lq收敛性，其中p是Khasminskii-型条件下的参数.
This paper establishes the convergence of a class of highly nonlinear stochastic differential delay equations without the linear growth condition replacing by Khasminskii-type condition, so the convergence criteria here may cover a wider class of nonlinear systems. Our aim is to propose the partially truncated Euler–Maruyama method for stochastic differential delay equations d y (t)= f (y (t), y (t− τ)) d t+ g (y (t), y (t− τ)) d w (t) and consider the strong-L q convergence for 2≤ q< p under the local Lipschitz condition plus Khasminskii-type condition, and p is a parameter in Khasminskii-type condition.