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Generalized two-step Maruyama methods for stochastic differential equations

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  • Ren, Quanwei
  • Tian, Hongjiong

Abstract

In this paper, we propose generalized two-step Maruyama methods for solving Itô stochastic differential equations. Numerical analysis concerning consistency, convergence and numerical stability in the mean-square sense is presented. We derive sufficient and necessary conditions for linear mean-square stability of the generalized two-step Maruyama methods. We compare the stability region of the generalized two-step Maruyama methods of Adams type with that of the corresponding two-step Maruyama methods of Adams type and show that our proposed methods have better linear mean-square stability. A numerical example is given to confirm our theoretical results.

Suggested Citation

  • Ren, Quanwei & Tian, Hongjiong, 2018. "Generalized two-step Maruyama methods for stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 48-57.
    • Handle: RePEc:eee:apmaco:v:332:y:2018:i:c:p:48-57
    DOI: 10.1016/j.amc.2018.03.003
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    References listed on IDEAS

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    1. P. E. Kloeden & Eckhard Platen, 1992. "Higher-order implicit strong numerical schemes for stochastic differential equations," Published Paper Series 1992-1, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
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    Cited by:

    1. D’Ambrosio, Raffaele & Scalone, Carmela, 2021. "Two-step Runge-Kutta methods for stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 403(C).

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