Variable-Step Euler–Maruyama Approximations of Regime-Switching Jump Diffusion Processes

Peng Chen (), Xinghu Jin (), Tian Shen () and Zhonggen Su ()
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Peng Chen: Nanjing University of Aeronautics and Astronautics
Xinghu Jin: Hefei University of Technology
Tian Shen: Zhejiang University
Zhonggen Su: Zhejiang University

Journal of Theoretical Probability, 2024, vol. 37, issue 2, 1597-1626

Abstract: Abstract Let $$\left( X_{t},Z_{t}\right) _{t\ge 0}$$ X t , Z t t ≥ 0 be the regime-switching jump diffusion process with invariant measure $$\mu $$ μ . We aim to approximate $$\mu $$ μ using the Euler–Maruyama (EM) scheme with decreasing step sequence $$\Gamma =(\gamma _n)_{n\in {\mathbb {N}}}$$ Γ = ( γ n ) n ∈ N . Under some appropriate dissipative conditions and uniform ellipticity assumptions on the coefficients of the related stochastic differential equation (SDE), we show that the error between $$\mu $$ μ and the invariant measure associated with the EM scheme is bounded by $$O(\sqrt{\gamma _n})$$ O ( γ n ) . In particular, we derive a better convergence rate $$O(\gamma _n)$$ O ( γ n ) for the additive case and the continuous case.

Keywords: Euler–Maruyama scheme; Decreasing step; Invariant measure; Regime-switching jump process; 60B10; 60G51; 60J25; 60J75 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-023-01253-w

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