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August 2003 Geometric ergodicity of discrete-time approximations to multivariate diffusions
Niels Richard Hansen
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Bernoulli 9(4): 725-743 (August 2003). DOI: 10.3150/bj/1066223276


A discrete-time approximation scheme called local linearization of the Langevin diffusion on Rk is considered, with emphasis on the ergodic properties of the approximation considered as a discrete-time Markov chain. We will derive criteria for the scheme to be geometrically ergodic, and illustrate the use of these criteria by means of examples. Furthermore, we discuss the scheme in relation to other schemes and the use of such discretization schemes as proposals in a Metropolis-Hastings algorithm.


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Niels Richard Hansen. "Geometric ergodicity of discrete-time approximations to multivariate diffusions." Bernoulli 9 (4) 725 - 743, August 2003.


Published: August 2003
First available in Project Euclid: 15 October 2003

zbMATH: 1044.60067
MathSciNet: MR1996277
Digital Object Identifier: 10.3150/bj/1066223276

Keywords: geometric drift , geometric ergodicity , Langevin diffusions , Markov chain Monte Carlo , Markov chains , Stochastic differential equations

Rights: Copyright © 2003 Bernoulli Society for Mathematical Statistics and Probability

Vol.9 • No. 4 • August 2003
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