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Convergence of the Euler Method of Stochastic Differential Equations with Piecewise Continuous Arguments

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  • Ling Zhang
  • Minghui Song

Abstract

The main purpose of this paper is to investigate the strong convergence of the Euler method to stochastic differential equations with piecewise continuous arguments (SEPCAs). Firstly, it is proved that the Euler approximation solution converges to the analytic solution under local Lipschitz condition and the bounded th moment condition. Secondly, the Euler approximation solution converge to the analytic solution is given under local Lipschitz condition and the linear growth condition. Then an example is provided to show which is satisfied with the monotone condition without the linear growth condition. Finally, the convergence of numerical solutions to SEPCAs under local Lipschitz condition and the monotone condition is established.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlaaa:643783
    DOI: 10.1155/2012/643783
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    Cited by:

    1. 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.

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