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Convergence of numerical solutions to stochastic differential equations with Markovian switching

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  • Fan, Zhencheng

Abstract

The paper develops strong approximation schemes for solutions of stochastic differential equations with Markovian switching (SDEwMSs). The convergent orders of existing strong numerical schemes all are 0.5. This paper provides a convergence theorem for the construction of strong approximations of any given order of convergence for SDEwMSs, and then constructs the order 1 scheme, the order 1.5 scheme.

Suggested Citation

  • Fan, Zhencheng, 2017. "Convergence of numerical solutions to stochastic differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 176-187.
    • Handle: RePEc:eee:apmaco:v:315:y:2017:i:c:p:176-187
    DOI: 10.1016/j.amc.2017.07.061
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    References listed on IDEAS

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    1. Yuan, Chenggui & Mao, Xuerong, 2004. "Convergence of the Euler–Maruyama method for stochastic differential equations with Markovian switching," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(2), pages 223-235.
    2. NicolaBruti-Liberati & Eckhard Platen, 2007. "Strong approximations of stochastic differential equations with jumps," Published Paper Series 2007-7, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    3. Mao, Xuerong, 1999. "Stability of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 45-67, January.
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    Cited by:

    1. Yang Li & Taitao Feng & Yaolei Wang & Yifei Xin, 2021. "A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models," Mathematics, MDPI, vol. 9(6), pages 1-15, March.

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