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

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

Mathematics, 2024, vol. 12, issue 12, 1-17

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.

Keywords: state-dependent regime switching; rate of convergence; Euler–Maruyama method; non-Lipschitz (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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