Delay dependent stability of stochastic split-step θ methods for stochastic delay differential equations

Hu, Ping; Huang, Chengming

doi:10.1016/j.amc.2018.07.064

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Cited by 3 publications

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“…Secondly, the requirement on the step size of the method is significantly released compared with the existing works, which is a stand-alone interesting result. It should be mentioned that many other interesting numerical methods have been proposed for SDDEs, for example [1,2,3,4,8,9,11,10,17,18,23] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Equivalence of pth moment stability between stochastic differential delay equations and their numerical methods

Bao

Tang

Shen

et al. 2019

Preprint

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In this paper, a general theorem on the equivalence of pth moment stability between stochastic differential delay equations (SDDEs) and their numerical methods is proved under the assumptions that the numerical methods are strongly convergent and have the bouneded pth moment in the finite time. The truncated Euler-Maruyama (EM) method is studied as an example to illustrate that the theorem indeed covers a large ranges of SDDEs. Alongside the investigation of the truncated EM method, the requirements on the step size of the method are significantly released compared with the work, where the method was initially proposed.

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