The Euler-Maruyama Approximation of State-Dependent Regime Switching Diffusions

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

Journal of Theoretical Probability, 2025, vol. 38, issue 1, 1-40

Abstract: Abstract In this paper, we consider the state-dependent regime switching diffusion process $$(X(t), R(t))_{t \geqslant 0}$$ ( X ( t ) , R ( t ) ) t ⩾ 0 , where the drift term does not necessarily satisfy the dissipative condition for certain states of the switching component. We develop delicately the Lindeberg replacement trick and a change-of-measure technique to obtain the convergence rate between the law of $$(X(t), R(t))_{t\geqslant 0}$$ ( X ( t ) , R ( t ) ) t ⩾ 0 and that of its Euler-Maruyama scheme with constant and decreasing step sizes. This convergence rate is quantified in terms of a function-class distance $$d_{\mathcal {G}}$$ d G . Moreover, we establish the ergodicity property of the Euler-Maruyama scheme. To illustrate our theoretical findings, we present in detail an example.

Keywords: Change of measure; Euler-Maruyama scheme; Jacobi flow; Lindeberg principle; M-matrix; Random switching with dependent state; Skorokhod’s representation; 60B10; 60G51; 60J25; 60J75 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-024-01379-5

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