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Likelihood ratio gradient estimation for stochastic recursions

Part of: Special processes Stochastic processes Probabilistic methods, simulation and stochastic differential equations Markov processes

Published online by Cambridge University Press:  01 July 2016

Peter W. Glynn  and
Pierre L'ecuyer
Peter W. Glynn*
Affiliation:
Stanford University
Pierre L'ecuyer*
Affiliation:
Université de Montréal
*
* Postal address: Department of Operations Research, Stanford University, Stanford, CA 94305-4022, USA.
** Postal address: Département d'IRO, Université de Montréal, C.P. 6128, Succ. Centre Ville, Montréal, H3C 3J7, Canada.
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Abstract

In this paper, we develop mathematical machinery for verifying that a broad class of general state space Markov chains reacts smoothly to certain types of perturbations in the underlying transition structure. Our main result provides conditions under which the stationary probability measure of an ergodic Harris-recurrent Markov chain is differentiable in a certain strong sense. The approach is based on likelihood ratio ‘change-of-measure' arguments, and leads directly to a ‘likelihood ratio gradient estimator' that can be computed numerically.

Keywords

HARRIS-RECURRENT MARKOV CHAINREGENERATION

MSC classification

Primary: 60K05: Renewal theory 60J27: Continuous-time Markov processes on discrete state spaces 65C05: Monte Carlo methods
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60G30: Continuity and singularity of induced measures 60G40: Stopping times; optimal stopping problems; gambling theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 27 , Issue 4 , December 1995 , pp. 1019 - 1053
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

The research of this author was supported by the U.S. Army Research Office under Contract No. DAAL03-91-G-0101 and by the National Science Foundation under Contract No. DDM-9101580.

This author's research was supported by NSERC-Canada grant No. OGPO110050 and FCAR-Québec Grant No. 93ER-1654.

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