Polynomial convergence for reversible jump processes

Hui-Hui Cheng and Yong-Hua Mao

Statistics & Probability Letters, 2021, vol. 173, issue C

Abstract: We show how to use the polynomial integrability of hitting times and a type of local Poincaré inequality to obtain the Liggett–Stroock inequality, which is used to study the polynomial convergence rate for reversible jump process. In fact, the polynomial integrability of hitting times on a subset implies that the taboo process restricted on its complement set decays polynomially, by which we get the Liggett–Stroock inequality with absorbing (Dirichlet) boundary. Using it and local Poincaré inequality, the explicit constant in the Liggett–Stroock inequality and a quantitative estimate for polynomial convergence rate in the sense of ‖Pt−π‖∞→2 are obtained.

Keywords: Polynomial convergence; Jump process; Liggett–Stroock inequality (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2021.109081

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