Using Stein’s Method to Analyze Euler–Maruyama Approximations of Regime-Switching Jump Diffusion Processes

Xinghu Jin (), Tian Shen () and Zhonggen Su ()
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Xinghu Jin: Hefei University of Technology
Tian Shen: Zhejiang University
Zhonggen Su: Zhejiang University

Journal of Theoretical Probability, 2023, vol. 36, issue 3, 1797-1828

Abstract: Abstract For a kind of regime-switching jump diffusion process $$(X_t,Z_t)_{t\ge 0}$$ ( X t , Z t ) t ≥ 0 , under some conditions, it is exponentially ergodic under the weighted total variation distance with ergodic measure $$\mu $$ μ . We use the Euler–Maruyama scheme of the process $$(X_t,Z_t)_{t\ge 0}$$ ( X t , Z t ) t ≥ 0 which has an ergodic measure $$\mu _{\eta }$$ μ η ( $$\eta $$ η is the step size of the Euler–Maruyama scheme) to approximate the ergodic measure $$\mu $$ μ . Furthermore, we use Stein’s method to prove that the convergence rate of $$\mu _{\eta }$$ μ η to $$\mu $$ μ is $$\eta ^{\frac{1}{2}}$$ η 1 2 in terms of some function-class distance $$d_{{\mathcal {G}}}(\mu ,\mu _{\eta })$$ d G ( μ , μ η ) .

Keywords: Euler–Maruyama scheme; Jacobi flow; Markovian switching; Poisson process; Stein’s equation; 60B10; 60G51; 60J25; 60J75 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-022-01221-w

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