Piecewise deterministic Markov processes and their invariant measures
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Publication:2077329
DOI10.1214/20-AIHP1125zbMATH Open1484.60083arXiv1807.05421MaRDI QIDQ2077329
Author name not available (Why is that?)
Publication date: 25 February 2022
Published in: (Search for Journal in Brave)
Abstract: Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which implies quantitative bounds on the total variation between the marginal distributions of the two processes. Finally two results are established regarding the invariant measures of PDMPs. A practical condition to show that a probability measure is invariant for the associated PDMP semi-group is presented. In a second time, a bound on the invariant probability measures in -norm of two PDMPs following the same differential flow is established. This last result is then applied to study the asymptotic bias of some non-exact PDMP MCMC methods.
Full work available at URL: https://arxiv.org/abs/1807.05421
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