## Electronic Communications in Probability

### Geometric Ergodicity and Perfect Simulation

Wilfrid Kendall

#### Abstract

This note extends the work of Foss and Tweedie (1998), who showed that availability of the classic Coupling from the Past (CFTP) algorithm of Propp and Wilson (1996) is essentially equivalent to uniform ergodicity for a Markov chain (see also Hobert and Robert, 2004). In this note we show that all geometrically ergodic chains possess dominated CFTP algorithms (not necessarily practical!) which are rather closely connected to Foster-Lyapunov criteria. Hence geometric ergodicity implies dominated CFTP.

#### Article information

Source
Electron. Commun. Probab. Volume 9 (2004), paper no. 15, 140-151.

Dates
Accepted: 26 October 2004
First available in Project Euclid: 26 May 2016

http://projecteuclid.org/euclid.ecp/1464286695

Digital Object Identifier
doi:10.1214/ECP.v9-1117

Mathematical Reviews number (MathSciNet)
MR2108860

Subjects
Primary: 60J05: Discrete-time Markov processes on general state spaces

Rights

#### Citation

Kendall, Wilfrid. Geometric Ergodicity and Perfect Simulation. Electron. Commun. Probab. 9 (2004), paper no. 15, 140--151. doi:10.1214/ECP.v9-1117. http://projecteuclid.org/euclid.ecp/1464286695.

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