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A note on the polynomial ergodicity of the one-dimensional Zig-Zag process

Part of: Markov processes Limit theorems Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  18 July 2022

Giorgos Vasdekis  and
Gareth O. Roberts
Giorgos Vasdekis*
Affiliation:
University of Warwick
Gareth O. Roberts*
Affiliation:
University of Warwick
*
*Postal address: Department of Statistics, University of Warwick, Coventry, CV4 7AL, UK.
*Postal address: Department of Statistics, University of Warwick, Coventry, CV4 7AL, UK.
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Abstract

We prove polynomial ergodicity for the one-dimensional Zig-Zag process on heavy-tailed targets and identify the exact order of polynomial convergence of the process when targeting Student distributions.

Keywords

Piecewise deterministic Markov processMarkov chain Monte Carlopolynomial ergodicity

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 65C05: Monte Carlo methods 60F05: Central limit and other weak theorems
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 3 , September 2022 , pp. 895 - 903
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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