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pth moment (p∈(0,1)) and almost sure exponential stability of the exact solutions and modified truncated EM method for stochastic differential equations

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  • Lan, Guangqiang
  • Xia, Fang
  • Zhao, Mei

Abstract

Exponential stability of exact solutions and modified truncated Euler–Maruyama method for stochastic differential equations are investigated in this paper. Sufficient conditions for the pth moment (p∈(0,1)) and almost sure exponential stability of both the exact solution and the given numerical method are presented. An example is provided to support our conclusions.

Suggested Citation

  • Lan, Guangqiang & Xia, Fang & Zhao, Mei, 2020. "pth moment (p∈(0,1)) and almost sure exponential stability of the exact solutions and modified truncated EM method for stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 160(C).
  • Handle: RePEc:eee:stapro:v:160:y:2020:i:c:s0167715220300043
    DOI: 10.1016/j.spl.2020.108701
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    References listed on IDEAS

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    1. Chen, Lin & Wu, Fuke, 2012. "Almost sure exponential stability of the θ-method for stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 82(9), pages 1669-1676.
    2. Lan, Guangqiang & Wu, Jiang-Lun, 2014. "New sufficient conditions of existence, moment estimations and non confluence for SDEs with non-Lipschitzian coefficients," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4030-4049.
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