Electronic Journal of Probability

Quantitative Bounds for Convergence Rates of Continuous Time Markov Processes

Gareth Roberts and Jeffrey Rosenthal

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1453756472

Digital Object Identifier
doi:10.1214/EJP.v1-9

Mathematical Reviews number (MathSciNet)
MR1423462

Zentralblatt MATH identifier
0891.60068

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

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

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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