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Simulation from quasi-stationary distributions on reducible state spaces

Part of: Nonparametric inference Markov processes

Published online by Cambridge University Press:  08 September 2017

A. Griffin ,
P. A. Jenkins ,
G. O. Roberts  and
S. E. F. Spencer
A. Griffin*
Affiliation:
University of Warwick
P. A. Jenkins*
Affiliation:
University of Warwick
G. O. Roberts*
Affiliation:
University of Warwick
S. E. F. Spencer*
Affiliation:
University of Warwick
*
* Postal address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.
* Postal address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.
* Postal address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.
* Postal address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.
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Abstract

Quasi-stationary distributions (QSDs) arise from stochastic processes that exhibit transient equilibrium behaviour on the way to absorption. QSDs are often mathematically intractable and even drawing samples from them is not straightforward. In this paper the framework of sequential Monte Carlo samplers is utilised to simulate QSDs and several novel resampling techniques are proposed to accommodate models with reducible state spaces, with particular focus on preserving particle diversity on discrete spaces. Finally, an approach is considered to estimate eigenvalues associated with QSDs, such as the decay parameter.

Keywords

Quasi-stationary distributionlimiting conditional distributionsimulationresampling methodsequential Monte Carlo

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 62G09: Resampling methods
Type
Research Article
Information
Advances in Applied Probability , Volume 49 , Issue 3 , September 2017 , pp. 960 - 980
Copyright
Copyright © Applied Probability Trust 2017 

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