On the time to extinction from quasi-stationarity: A unified approach
| dc.contributor.author | Artalejo Rodríguez, Jesús Manuel | |
| dc.date.accessioned | 2023-06-20T00:15:58Z | |
| dc.date.available | 2023-06-20T00:15:58Z | |
| dc.date.issued | 2012-10 | |
| dc.description.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. | |
| dc.description.department | Depto. de Estadística e Investigación Operativa | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/16316 | |
| dc.identifier.doi | 10.1016/j.physa.2012.05.004 | |
| dc.identifier.issn | 0378-4371 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0378437112003603 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/42297 | |
| dc.issue.number | 19 | |
| dc.journal.title | Physica A: Statistical Mechanics and its Applications | |
| dc.language.iso | eng | |
| dc.page.final | 4486 | |
| dc.page.initial | 4483 | |
| dc.publisher | Elsevier | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 519.22 | |
| dc.subject.keyword | Time to extinction | |
| dc.subject.keyword | Quasi-stationarity | |
| dc.subject.keyword | Epidemic | |
| dc.subject.keyword | Markov chain | |
| dc.subject.ucm | Estadística matemática (Matemáticas) | |
| dc.subject.unesco | 1209 Estadística | |
| dc.title | On the time to extinction from quasi-stationarity: A unified approach | |
| dc.type | journal article | |
| dc.volume.number | 391 | |
| dcterms.references | L.J.S. Allen, An Introduction to Stochastic Processes with Applications to Biology, Prentice-Hall, New Jersey, 2003. N.G. van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland, Amsterdam, 1992. M.M. de Oliveira, R. Dickman, Quasi-stationary distributions for models of heterogeneous catalysis, Physica A 343 (2004) 525–542. S.A. Hassan, M.A. Ingram, A quasi-stationary Markov chain model of a cooperative multi-hop linear network, IEEE Trans. Wireless Commun. 10 (2011) 2306–2315. R. Dickman, M.M. de Oliveira, Quasi-stationary simulation of the contact process, Physica A 357 (2005) 134–141. A. Pinto, M. Aguiar, J. Martins, N. Stollenwerk, Dynamics of epidemiological models, Acta Biotheor. 58 (2010) 381–389. S. Kalpakam, On the quasi-stationary distribution of the residual lifetime, IEEE Trans. Reliab. 42 (1993) 623–624. J.R. Artalejo, M.J. Lopez-Herrero, Quasi-stationarity and ratio of expectations distributions: a comparative study, J. Theoret. Biol. 266 (2010) 264–274. H. Andersson, T. Britton, Stochastic Epidemic Models and Their Statistical Analysis, in: Lecture Notes in Statistics, vol. 151, Springer, New York, 2000. I. Nåsell, On the quasi-stationary distribution of the stochastic logistic epidemic, Math. Biosci. 156 (1999) 21–40. I. Nåsell, Extinction and quasi-stationarity in the Verhulst logistic model, J. Theoret. Biol. 211 (2001) 11–27. R.H. Norden, On the distribution of the time to extinction in the stochastic logistic population model, Adv. Appl. Prob. 14 (1982) 687–708. H. Andersson, T. Britton, Stochastic epidemics in dynamic populations: quasi-stationarity and extinction, J. Math. Biol. 41 (2000) 559–580. J.R. Artalejo, A. Gomez-Corral, Q.M. He, Markovian arrivals in stochastic modeling: a survey and some new results, SORT 34 (2010) 101–144. P. Andersson, D. Lindenstrand, A stochastic SIS epidemic with demography: initial stages and time to extinction, J. Math. Biol. 62 (2011) 333–348. I. Nåsell, A new look at the critical community size for childhood infections, Theor. Popul. Biol. 67 (2005) 203–216. .N. Darroch, E. Seneta, On quasi-stationary distributions in absorbing discrete-time finite Markov chains, J. Appl. Prob. 2 (1965) 88–100. J.N. Darroch, E. Seneta, On quasi-stationary distributions in absorbing continuous-time finite Markov chains, J. Appl. Prob. 4 (1967) 192–196. E.A. van Doorn, P.K. Pollett, Survival in a quasi-death process, Linear Algebra Appl. 429 (2008) 776–791. E.A. van Doorn, P.K. Pollett, Quasi-stationary distributions for reducible absorbing chains in discrete time, Markov Processes Relat. Fields 15 (2009) 191–204. M.G. Nair, P.K. Pollett, On the relationship between μ-invariant measures and quasi-stationary distributions for continuous-time Markov chains, Adv. Appl. Prob. 25 (1993) 82–102. P. Coolen-Schrijner, E.A. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | db4b8a04-44b0-48e9-8b2c-c80ffae94799 | |
| relation.isAuthorOfPublication.latestForDiscovery | db4b8a04-44b0-48e9-8b2c-c80ffae94799 |
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