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1996 Quantitative Bounds for Convergence Rates of Continuous Time Markov Processes
Gareth Roberts, Jeffrey Rosenthal
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Electron. J. Probab. 1: 1-21 (1996). DOI: 10.1214/EJP.v1-9


We develop quantitative bounds on rates of convergence for continuous-time Markov processes on general state spaces. Our methods involve coupling and shift-coupling, and make use of minorization and drift conditions. In particular, we use auxiliary coupling to establish the existence of small (or pseudo-small) sets. We apply our method to some diffusion examples. We are motivated by interest in the use of Langevin diffusions for Monte Carlo simulation.


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Gareth Roberts. Jeffrey Rosenthal. "Quantitative Bounds for Convergence Rates of Continuous Time Markov Processes." Electron. J. Probab. 1 1 - 21, 1996.


Accepted: 28 May 1996; Published: 1996
First available in Project Euclid: 25 January 2016

zbMATH: 0891.60068
MathSciNet: MR1423462
Digital Object Identifier: 10.1214/EJP.v1-9

Primary: 60J25

Keywords: coupling , drift condition , Markov process , minorization condition , rates of convergence , Shift-coupling

Vol.1 • 1996
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