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Volumn 11, Issue 1, 2001, Pages 261-284

Asymptotic behavior of absorbing Markov chains conditional on nonabsorption for applications in conservation biology

Author keywords

Absorbing set; Density dependence population size dependent Bienaym Galton Watson branching processes; Extinction; Homogeneous Markov chain; Nonnegative operator; Quasi compact linear operator; Quasi stationary distribution; Yaglom limit

Indexed keywords


EID: 0035593503     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/998926993     Document Type: Article
Times cited : (36)

References (38)
  • 2
    • 0000546035 scopus 로고
    • Branching processes with random environments. I. Extinction probabilities
    • ATHREYA, K. B. and KARLIN, S. (1971). Branching processes with random environments. I. extinction probabilities. Ann. Math. Statist. 42 1499-1520. II. limit theorems. Ann. Math. Statist. 42 1843-1858.
    • (1971) Ann. Math. Statist. , vol.42 , pp. 1499-1520
    • Athreya, K.B.1    Karlin, S.2
  • 3
    • 0011355047 scopus 로고    scopus 로고
    • Branching processes with random environments. II. Limit theorems
    • ATHREYA, K. B. and KARLIN, S. (1971). Branching processes with random environments. I. extinction probabilities. Ann. Math. Statist. 42 1499-1520. II. limit theorems. Ann. Math. Statist. 42 1843-1858.
    • Ann. Math. Statist. , vol.42 , pp. 1843-1858
  • 5
    • 0013478051 scopus 로고
    • Quelques applications probabilistes de la quasi compacité
    • BRUNEL, A. and REVUZ, D. (1974). Quelques applications probabilistes de la quasi compacité. Ann. Inst. H. Poincaré Sec. B 10 301-337.
    • (1974) Ann. Inst. H. Poincaré Sec. B , vol.10 , pp. 301-337
    • Brunel, A.1    Revuz, D.2
  • 6
    • 0016487777 scopus 로고
    • On quasi-stationary distributions for multitype Galton-Watson processes
    • BUICULESCU, M. (1975). On quasi-stationary distributions for multitype Galton-Watson processes. J. Appl. Probab. 12 60-68.
    • (1975) J. Appl. Probab. , vol.12 , pp. 60-68
    • Buiculescu, M.1
  • 9
    • 0030502869 scopus 로고    scopus 로고
    • R-positivity, quasi-stationary distributions and ratio limit theorems for a class of probabilistic automata
    • FERRARI, P. A., KESTEN, H. and MARTINEZ, S. (1996). R-positivity, quasi-stationary distributions and ratio limit theorems for a class of probabilistic automata. Ann. Appl. Probab. 6 577-616.
    • (1996) Ann. Appl. Probab. , vol.6 , pp. 577-616
    • Ferrari, P.A.1    Kesten, H.2    Martinez, S.3
  • 10
    • 0002962742 scopus 로고
    • On the stochastic matrices associated with certain queuing processes
    • FOSTER, F. G. (1953). On the stochastic matrices associated with certain queuing processes. Ann. Math. Statist. 24 355-360.
    • (1953) Ann. Math. Statist. , vol.24 , pp. 355-360
    • Foster, F.G.1
  • 11
    • 0009254676 scopus 로고
    • Controlled Galton-Watson process and its asymptotic behaviour
    • FUJIMAGARI, T. (1976). Controlled Galton-Watson process and its asymptotic behaviour. KodaïMath. Sem. Rep. 27 11-18.
    • (1976) KodaïMath. Sem. Rep. , vol.27 , pp. 11-18
    • Fujimagari, T.1
  • 16
    • 0002007604 scopus 로고
    • On some classes of population-size-dependent Galton-Watson processes
    • HÖPFNER, R. (1985). On some classes of population-size-dependent Galton-Watson processes. J. Appl. Probab. 22 25-36.
    • (1985) J. Appl. Probab. , vol.22 , pp. 25-36
    • Höpfner, R.1
  • 17
    • 0039269396 scopus 로고
    • Some results on population-size-dependent Galton-Watson processes
    • HÖPFNER, R. (1986). Some results on population-size-dependent Galton-Watson processes. J. Appl. Probab. 23 297-306.
    • (1986) J. Appl. Probab. , vol.23 , pp. 297-306
    • Höpfner, R.1
  • 18
    • 0039861094 scopus 로고
    • Analytical methods for discrete branching processes
    • A. Joffe and P. Ney, eds. Dekker, New York
    • HOPPE, F. M. and SENETA, E. (1978). Analytical methods for discrete branching processes. In Branching Processes. Advances in Probability and Related Topics (A. Joffe and P. Ney, eds.) 5 219-261. Dekker, New York.
    • (1978) Branching Processes. Advances in Probability and Related Topics , vol.5 , pp. 219-261
    • Hoppe, F.M.1    Seneta, E.2
  • 21
    • 0038227478 scopus 로고
    • On multitype branching processes with ρ ≤ 1
    • JOFFE, A. and SPITZER, F. (1967). On multitype branching processes with ρ ≤ 1. J. Math. Anal. Appl. 19 409-430.
    • (1967) J. Math. Anal. Appl. , vol.19 , pp. 409-430
    • Joffe, A.1    Spitzer, F.2
  • 24
    • 0001101077 scopus 로고
    • A ratio limit theorem for (sub) Markov chains on {1, 2, . . .} with bounded jumps
    • KESTEN, H. (1995). A ratio limit theorem for (sub) Markov chains on {1, 2, . . .} with bounded jumps. Adv. in Appl. Probab. 27 652-691.
    • (1995) Adv. in Appl. Probab. , vol.27 , pp. 652-691
    • Kesten, H.1
  • 25
    • 0001814148 scopus 로고
    • On population-size-dependent branching processes
    • KLEBANER, F. C. (1984). On population-size-dependent branching processes. Adv. in Appl. Probab. 16 30-55.
    • (1984) Adv. in Appl. Probab. , vol.16 , pp. 30-55
    • Klebaner, F.C.1
  • 26
    • 0002306055 scopus 로고
    • A limit theorem for population-size-dependent branching processes
    • KLEBANER, F. C. (1985). A limit theorem for population-size-dependent branching processes. J. Appl. Probab. 22 48-57.
    • (1985) J. Appl. Probab. , vol.22 , pp. 48-57
    • Klebaner, F.C.1
  • 27
    • 0002945715 scopus 로고
    • Linear operators leaving invariant a cone in a Banach space
    • KREIN, M. G. and RUTMAN, M. A. (1950). Linear operators leaving invariant a cone in a Banach space. Uspehi Mat. Nauk. 3. (English translation in Amer. Math. Soc. Transl. 10 199-325.)
    • (1950) Uspehi Mat. Nauk. , vol.3
    • Krein, M.G.1    Rutman, M.A.2
  • 28
    • 0000315972 scopus 로고    scopus 로고
    • English translation in
    • KREIN, M. G. and RUTMAN, M. A. (1950). Linear operators leaving invariant a cone in a Banach space. Uspehi Mat. Nauk. 3. (English translation in Amer. Math. Soc. Transl. 10 199-325.)
    • Amer. Math. Soc. Transl. , vol.10 , pp. 199-325
  • 29
    • 0003586898 scopus 로고
    • Contribution à la dynamique des populations d'oiseaux
    • Ph.D. thesis, Univ. Lyon 1, France
    • LEBRETON, J.-D. (1981). Contribution à la dynamique des populations d'oiseaux. Modèles mathématiques en temps discret. Ph.D. thesis, Univ. Lyon 1, France.
    • (1981) Modèles Mathématiques en Temps Discret
    • Lebreton, J.-D.1
  • 30
    • 0010346868 scopus 로고
    • Sur le comportement asymptotique des probabilités dans les ensembles des états d'une chaîne de Markov homogène
    • in Russian
    • MANDL, P. (1959). Sur le comportement asymptotique des probabilités dans les ensembles des états d'une chaîne de Markov homogène. Časopis Pěst. Mat 84 140-149 (in Russian).
    • (1959) Časopis Pěst. Mat , vol.84 , pp. 140-149
    • Mandl, P.1
  • 31
    • 0002849451 scopus 로고
    • Gambling for existence
    • REDDINGIUS, J. (1971). Gambling for existence. Acta Biotheoretica 20 (suppl.) 1-208.
    • (1971) Acta Biotheoretica , vol.20 , Issue.SUPPL. , pp. 1-208
    • Reddingius, J.1
  • 32
    • 84972502094 scopus 로고
    • Quasi-positive operators
    • SASSER, D. W. (1964). Quasi-positive operators. Pacific J. Math. 14 1029-1037.
    • (1964) Pacific J. Math. , vol.14 , pp. 1029-1037
    • Sasser, D.W.1
  • 34
    • 0000564723 scopus 로고
    • On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states
    • SENETA, E. and VERB-JONES, D. (1966). On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states. J. Appl. Probab. 3 403-434.
    • (1966) J. Appl. Probab. , vol.3 , pp. 403-434
    • Seneta, E.1    Verb-Jones, D.2
  • 35
    • 0011611270 scopus 로고
    • On multitype branching processes in a random environment
    • TANNY, D. (1981). On multitype branching processes in a random environment. Adv. in Appl. Probab. 13 464-497.
    • (1981) Adv. in Appl. Probab. , vol.13 , pp. 464-497
    • Tanny, D.1
  • 37
    • 84972513565 scopus 로고
    • Ergodic properties of nonnegative matrices I
    • VERE-JONES, D. (1967). Ergodic properties of nonnegative matrices I. Pacific J. Math. 22 361-386.
    • (1967) Pacific J. Math. , vol.22 , pp. 361-386
    • Vere-Jones, D.1
  • 38
    • 84972574281 scopus 로고
    • Ergodic properties of nonnegative matrices II
    • VERE-JONES, D. (1968). Ergodic properties of nonnegative matrices II. Pacific J. Math. 26 601-620.
    • (1968) Pacific J. Math. , vol.26 , pp. 601-620
    • Vere-Jones, D.1


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