Almost sure exponential stability of the Milstein-type schemes for stochastic delay differential equations

Rong Hu

Chaos, Solitons & Fractals, 2020, vol. 131, issue C

Abstract: This paper investigates the almost sure exponential stability of Milstein-type schemes for stochastic delay differential equations (SDDEs) using the discrete semimartingale convergence theorem. It is shown that the Milstein scheme can preserve the almost sure stability of the exact solution under a linear growth condition on the drift. If the drift defies the linear growth condition, but satisfies a one-sided Lipschitz condition, we show backward Milstein scheme can share the almost sure exponential stability. Moreover, the exponential decay rates of the two classes of Milstein schemes are also investigated. Numerical experiments are performed to confirm our theoretic findings.

Keywords: Milstein method; Backward milstein method; Almost sure exponential stability (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:131:y:2020:i:c:s096007791930445x

DOI: 10.1016/j.chaos.2019.109499

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