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Simulation from quasi-stationary distributions on reducible state spaces

  • A. Griffin (a1), P. A. Jenkins (a1), G. O. Roberts (a1) and S. E. F. Spencer (a1)

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.

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* Postal address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.
** Current address: Centre for Ecology and Hydrology, Maclean Building, Benson Lane, Crowmarsh Gifford, Wallingford, Oxfordshire OX10 8BB. Email address:
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
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