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Strong convergence of explicit schemes for highly nonlinear stochastic differential equations with Markovian switching

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  • Zhao, Jingjun
  • Yi, Yulian
  • Xu, Yang

Abstract

Two projected Euler type schemes are analyzed for stochastic differential equations with Markovian switching whose coefficients are super-linear. Under the polynomial growth condition and the monotone condition, we investigate the convergence in mean square sense of these numerical methods. Besides, we also discuss the convergence rates of these two schemes for highly nonlinear equations (including stochastic differential equations with and without Markovian switching) with small noise. Finally, some numerical experiments are given to verify our theoretical results.

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  • 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).
    • Handle: RePEc:eee:apmaco:v:398:y:2021:i:c:s0096300321000072
    DOI: 10.1016/j.amc.2021.125959
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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. Li, Min & Huang, Chengming, 2020. "Projected Euler-Maruyama method for stochastic delay differential equations under a global monotonicity condition," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    3. Zhao, Jingjun & Yi, Yulian & Xu, Yang, 2019. "Mean square convergence of explicit two-step methods for highly nonlinear stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 466-483.
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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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