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Approximations of the Euler–Maruyama Method of Stochastic Differential Equations with Regime Switching

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  • Yuhang Zhen

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China)

Abstract

This work focuses on a class of regime-switching diffusion processes with both continuous components and discrete components. Under suitable conditions, we adopt the Euler–Maruyama method to deal with the convergence of numerical solutions of the corresponding stochastic differential equations. More precisely, we first show the convergence rates in the L p -norm of the stochastic differential equations with regime switching under Lipschitz conditions. Then, we also discuss L 1 and L 2 convergence under non-Lipschitz conditions.

Suggested Citation

  • Yuhang Zhen, 2024. "Approximations of the Euler–Maruyama Method of Stochastic Differential Equations with Regime Switching," Mathematics, MDPI, vol. 12(12), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1819-:d:1413049
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    References listed on IDEAS

    as
    1. Ruihua Liu, 2014. "Optimal Investment and Consumption with Proportional Transaction Costs in Regime-Switching Model," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 614-641, November.
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