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Quantitative bounds for convergence rates of continuous time Markov processes. (English) Zbl 0891.60068

Summary: 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.

MSC:

60J25 Continuous-time Markov processes on general state spaces
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