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April 2021 Regeneration-enriched Markov processes with application to Monte Carlo
Andi Q. Wang, Murray Pollock, Gareth O. Roberts, David Steinsaltz
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Ann. Appl. Probab. 31(2): 703-735 (April 2021). DOI: 10.1214/20-AAP1602

Abstract

We study a class of Markov processes that combine local dynamics, arising from a fixed Markov process, with regenerations arising at a state-dependent rate. We give conditions under which such processes possess a given target distribution as their invariant measures, thus making them amenable for use within Monte Carlo methodologies. Since the regeneration mechanism can compensate the choice of local dynamics, while retaining the same invariant distribution, great flexibility can be achieved in selecting local dynamics, and the mathematical analysis is simplified. We give straightforward conditions for the process to possess a central limit theorem, and additional conditions for uniform ergodicity and for a coupling from the past construction to hold, enabling exact sampling from the invariant distribution. We further consider and analyse a natural approximation of the process which may arise in the practical simulation of some classes of continuous-time dynamics.

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Andi Q. Wang. Murray Pollock. Gareth O. Roberts. David Steinsaltz. "Regeneration-enriched Markov processes with application to Monte Carlo." Ann. Appl. Probab. 31 (2) 703 - 735, April 2021. https://doi.org/10.1214/20-AAP1602

Information

Received: 1 October 2019; Revised: 1 June 2020; Published: April 2021
First available in Project Euclid: 1 April 2021

Digital Object Identifier: 10.1214/20-AAP1602

Subjects:
Primary: 60J22 , 60J40
Secondary: 60J25 , 65C05

Keywords: Coupling from the past , inhomogeneous Poisson process , Markov chain Monte Carlo , regenerative Markov process , Right process

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.31 • No. 2 • April 2021
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