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On the time to extinction from quasi-stationarity: A unified approach

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  • Artalejo, J.R.

Abstract

This note provides a unified approach to the distribution of the time to extinction from quasi-stationarity for general Markov chains evolving both in discrete and in continuous time. Our results generalize a number of similar derivations which were established ad hoc for a variety of stochastic epidemic models. On the other hand, the obtained results unify the infinite irreducible case and the finite (reducible or irreducible) case which are typically presented under separate formulations in the literature for Markov chains.

Suggested Citation

  • Artalejo, J.R., 2012. "On the time to extinction from quasi-stationarity: A unified approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(19), pages 4483-4486.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:19:p:4483-4486
    DOI: 10.1016/j.physa.2012.05.004
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    References listed on IDEAS

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    1. de Oliveira, Marcelo M. & Dickman, Ronald, 2004. "Quasi-stationary distributions for models of heterogeneous catalysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 525-542.
    2. Dickman, Ronald & Martins de Oliveira, Marcelo, 2005. "Quasi-stationary simulation of the contact process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 357(1), pages 134-141.
    3. Pauline Coolen-Schrijner & Erik A. Doorn, 2006. "Quasi-stationary Distributions for a Class of Discrete-time Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 8(4), pages 449-465, December.
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    Cited by:

    1. van Doorn, Erik A. & Pollett, Philip K., 2013. "Quasi-stationary distributions for discrete-state models," European Journal of Operational Research, Elsevier, vol. 230(1), pages 1-14.
    2. He, Zhidong & Van Mieghem, Piet, 2018. "The spreading time in SIS epidemics on networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 317-330.

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