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Numerical approximation for nonlinear stochastic pantograph equations with Markovian switching

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  • Zhou, Shaobo
  • Hu, Yangzi

Abstract

The main aim of the paper is to prove that the implicit numerical approximation can converge to the true solution to highly nonlinear hybrid stochastic pantograph differential equation. After providing the boundedness of the exact solution, the paper proves that the backward Euler–Maruyama numerical method can preserve boundedness of moments, and the numerical approximation converges strongly to the true solution. Finally, the exponential stability criterion on the backward Euler–Maruyama scheme is given, and a high order example is provided to illustrate the main result.

Suggested Citation

  • Zhou, Shaobo & Hu, Yangzi, 2016. "Numerical approximation for nonlinear stochastic pantograph equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 126-138.
    • Handle: RePEc:eee:apmaco:v:286:y:2016:i:c:p:126-138
    DOI: 10.1016/j.amc.2016.03.040
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    References listed on IDEAS

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    1. Wu, Fuke & Hu, Shigeng, 2011. "Khasminskii-type theorems for stochastic functional differential equations with infinite delay," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1690-1694, November.
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    Cited by:

    1. Zhan, Weijun & Gao, Yan & Guo, Qian & Yao, Xiaofeng, 2019. "The partially truncated Euler–Maruyama method for nonlinear pantograph stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 109-126.

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