Stability of Partially Implicit Langevin Schemes and Their MCMC Variants

Bruno Casella, Gareth O. Roberts and Osnat Stramer

MPRA Paper from University Library of Munich, Germany

Abstract: A broad class of implicit or partially implicit time discretizations for the Langevin diffusion are considered and used as proposals for the Metropolis–Hastings algorithm. Ergodic properties of our proposed schemes are studied. We show that introducing implicitness in the discretization leads to a process that often inherits the convergence rate of the continuous time process. These contrast with the behavior of the naive or Euler–Maruyama discretization, which can behave badly even in simple cases. We also show that our proposed chains, when used as proposals for the Metropolis–Hastings algorithm, preserve geometric ergodicity of their implicit Langevin schemes and thus behave better than the local linearization of the Langevin diffusion. We illustrate the behavior of our proposed schemes with examples. Our results are described in detail in one dimension only, although extensions to higher dimensions are also described and illustrated.

Keywords: Langevin; diffusions; Ergodicity; Implicit; Euler; schemes:; discrete; approximation (search for similar items in EconPapers)
JEL-codes: C61 C63 (search for similar items in EconPapers)
Date: 2011-12-01
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in Methodology and Computing in Applied Probability 4.13(2011): pp. 835-854

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/95220/1/MPRA_paper_95220.pdf original version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:95220

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter (winter@lmu.de).