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Strong convergence and exponential stability of stochastic differential equations with piecewise continuous arguments for non-globally Lipschitz continuous coefficients

Author

Listed:
  • Yang, Huizi
  • Song, Minghui
  • Liu, Mingzhu

Abstract

The paper deals with a split-step θ-method for stochastic differential equations with piecewise continuous arguments (SEPCAs). The strong convergence of the method is proved under non-globally Lipschitz conditions. The exponential stability of the exact and numerical solutions is obtained. Some experiments are given to illustrate the conclusions.

Suggested Citation

  • Yang, Huizi & Song, Minghui & Liu, Mingzhu, 2019. "Strong convergence and exponential stability of stochastic differential equations with piecewise continuous arguments for non-globally Lipschitz continuous coefficients," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 111-127.
    • Handle: RePEc:eee:apmaco:v:341:y:2019:i:c:p:111-127
    DOI: 10.1016/j.amc.2018.08.037
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    References listed on IDEAS

    as
    1. Qiu, Qinwei & Liu, Wei & Hu, Liangjian & Mao, Xuerong & You, Surong, 2016. "Stabilization of stochastic differential equations with Markovian switching by feedback control based on discrete-time state observation with a time delay," Statistics & Probability Letters, Elsevier, vol. 115(C), pages 16-26.
    2. Ling Zhang & Minghui Song, 2012. "Convergence of the Euler Method of Stochastic Differential Equations with Piecewise Continuous Arguments," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-16, December.
    3. Baker, Christopher T. H. & Buckwar, Evelyn, 2001. "Exponential stability in p-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations," SFB 373 Discussion Papers 2001,94, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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