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The partially truncated Euler–Maruyama method for nonlinear pantograph stochastic differential equations

Author

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  • Zhan, Weijun
  • Gao, Yan
  • Guo, Qian
  • Yao, Xiaofeng

Abstract

This paper develops the partially truncated Euler–Maruyama method for a class of highly nonlinear pantograph stochastic differential equations under the generalized Khasminskii-type conditions. The order of Lp-convergence is obtained. Moreover, some almost sure polynomial stability and mean square polynomial stability criteria are established for the numerical solution. Numerical examples are provided to illustrate the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:109-126
    DOI: 10.1016/j.amc.2018.10.052
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    References listed on IDEAS

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    1. 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.
    2. You, Surong & Mao, Wei & Mao, Xuerong & Hu, Liangjian, 2015. "Analysis on exponential stability of hybrid pantograph stochastic differential equations with highly nonlinear coefficients," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 73-83.
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    Cited by:

    1. Wu, Hao & Hu, Junhao & Yuan, Chenggui, 2022. "Stability of numerical solution to pantograph stochastic functional differential equations," Applied Mathematics and Computation, Elsevier, vol. 431(C).

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