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Regeneration-enriched Markov processes with application to Monte Carlo

Lookup NU author(s): Dr Murray Pollock

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This is the authors' accepted manuscript of a working paper that has been published in its final definitive form by arXiv, 2020.

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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.


Publication metadata

Author(s): Wang AQ, Pollock M, Roberts GO, Steinsaltz D

Publication type: Working Paper

Publication status: Published

Journal: arXiv

Year: 2020

Publisher: arXiv

URL: https://arxiv.org/abs/1910.05037


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