Polynomial Convergence Rates of Piecewise Deterministic Markov Processes

Gareth O. Roberts () and Jeffrey S. Rosenthal ()
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Gareth O. Roberts: University of Warwick
Jeffrey S. Rosenthal: University of Toronto

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 1, 1-18

Abstract: Abstract We consider piecewise-deterministic Markov processes such as the Bouncy Particle sampler, on target densities with polynomial tails. Using direct drift condition methods, we provide bounds on the polynomial order of the processes’ convergence rate to stationary, on both one-dimensional and high-dimensional state spaces, in both total variation distance and f-norm.

Keywords: PDMP; MCMC; Bouncy Particle sampler; Zig Zag algorithm; Convergence rate; Polynomial convergence; Infinitesimal generator; Drift condition; Primary 60J25; Secondary 60J22 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11009-023-09977-2

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