Aysmptotic Behavior of Absorbing Markov Chains Conditional on Nonabsorption for Applications in Conservation Biology
Gosselin, Frèdèric
Ann. Appl. Probab., Tome 11 (2001) no. 2, p. 261-284 / Harvested from Project Euclid
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We find a Lyapunov-type sufficient condition for discrete-time Markov chains on a countable state space including an absorbing set to almost surely reach this absorbing set and to asymptotically stabilize conditional on nonabsorption. This result is applied to Bienaymè-Galton-Watson-like branching processes in which the offspring distribution depends on the current population size. This yields a generalization of the Yaglom limit. The techniques used mainly rely on the spectral theory of linear operators on Banach spaces and especially on the notion of quasi-compact linear operator.
Publié le : 2001-02-14
Classification:  homogeneous Markov chain,  extinction,  absorbing set,  quasi-stationary distribution,  Yaglom limit,  density-dependence,  population-size-dependent,  Bienaymè-Galton-Watson branching processes,  quasi-compact linear operator,  nonnegative operator,  irreducible matrix,  infinite dimensional matrix,  spectral theory,  conservation biology,  population viability analysis,  demography,  population dynamics,  Lyapunov-type condition,  60J10,  47B37,  47B65,  60J20,  60J85,  92D25 
@article{998926993,
     author = {Gosselin, Fr\`ed\`eric},
     title = {Aysmptotic Behavior of Absorbing Markov Chains Conditional on Nonabsorption for Applications in Conservation Biology},
     journal = {Ann. Appl. Probab.},
     volume = {11},
     number = {2},
     year = {2001},
     pages = { 261-284},
     language = {en},
     url = {http://dml.mathdoc.fr/item/998926993}
}

Gosselin, Frèdèric. Aysmptotic Behavior of Absorbing Markov Chains Conditional on Nonabsorption for Applications in Conservation Biology. Ann. Appl. Probab., Tome 11 (2001) no. 2, pp.  261-284. http://gdmltest.u-ga.fr/item/998926993/