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A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models

Author

Listed:
  • Yang Li

    (College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China)

  • Taitao Feng

    (College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China)

  • Yaolei Wang

    (College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China)

  • Yifei Xin

    (College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China)

Abstract

In this paper, we propose a new weak order 2.0 numerical scheme for solving stochastic differential equations with Markovian switching (SDEwMS). Using the Malliavin stochastic analysis, we theoretically prove that the new scheme has local weak order 3.0 convergence rate. Combining the special property of Markov chain, we study the effects from the changes of state space on the convergence rate of the new scheme. Two numerical experiments are given to verify the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:588-:d:514106
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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. Nicola Bruti-Liberati, 2007. "Numerical Solution of Stochastic Differential Equations with Jumps in Finance," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2007, January-A.
    3. Zhao, Jingjun & Yi, Yulian & Xu, Yang, 2021. "Strong convergence of explicit schemes for highly nonlinear stochastic differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 398(C).
    4. He, Hangfeng & Qi, Wenhai & Kao, Yonggui, 2021. "HMM-based adaptive attack-resilient control for Markov jump system and application to an aircraft model," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    5. Mao, Xuerong, 1999. "Stability of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 45-67, January.
    6. 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.
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