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Stability equivalence among stochastic differential equations and stochastic differential equations with piecewise continuous arguments and corresponding Euler-Maruyama methods

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  • Song, Minghui
  • Geng, Yidan
  • Liu, Mingzhu

Abstract

In this paper, we consider the equivalence of the pth moment exponential stability for stochastic differential equations (SDEs), stochastic differential equations with piecewise continuous arguments (SDEPCAs) and the corresponding Euler-Maruyama methods EMSDEs and EMSDEPCAs. We show that if one of the SDEPCAs, SDEs, EMSDEs and EMSDEPCAs is pth moment exponentially stable, then any of them is pth moment exponentially stable for a sufficiently small step size h and τ under the global Lipschitz assumption on the drift and diffusion coefficients.

Suggested Citation

  • Song, Minghui & Geng, Yidan & Liu, Mingzhu, 2021. "Stability equivalence among stochastic differential equations and stochastic differential equations with piecewise continuous arguments and corresponding Euler-Maruyama methods," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    • Handle: RePEc:eee:apmaco:v:400:y:2021:i:c:s0096300320307669
    DOI: 10.1016/j.amc.2020.125813
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    References listed on IDEAS

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    1. Liu, Linna & Mo, Haoyi & Deng, Feiqi, 2019. "Split-step theta method for stochastic delay integro-differential equations with mean square exponential stability," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 320-328.
    2. You, Surong & Hu, Liangjian & Mao, Wei & Mao, Xuerong, 2015. "Robustly exponential stabilization of hybrid uncertain systems by feedback controls based on discrete-time observations," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 8-16.
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