Electronic Journal of Probability

Quantitative Bounds for Convergence Rates of Continuous Time Markov Processes

Gareth Roberts and Jeffrey Rosenthal

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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.

Article information

Electron. J. Probab., Volume 1 (1996), paper no. 9, 21 pp.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J25: Continuous-time Markov processes on general state spaces

Markov process rates of convergence coupling shift-coupling minorization condition drift condition

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Roberts, Gareth; Rosenthal, Jeffrey. Quantitative Bounds for Convergence Rates of Continuous Time Markov Processes. Electron. J. Probab. 1 (1996), paper no. 9, 21 pp. doi:10.1214/EJP.v1-9. https://projecteuclid.org/euclid.ejp/1453756472

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