메뉴 건너뛰기




Volumn 37, Issue 5, 2009, Pages 1926-1969

Quasi-stationary distributions and diffusion models in population dynamics

Author keywords

Birth death process; Convergence rate; Entrance boundary at infinity; Generalized Feller diffusion; Logistic growth; Population dynamics; Q process; Quasi stationary distribution; Yaglom limit

Indexed keywords


EID: 77149161730     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/09-AOP451     Document Type: Article
Times cited : (138)

References (31)
  • 3
    • 0000103738 scopus 로고
    • Asymptotic laws for onedimensional diffusions conditioned to nonabsorption
    • COLLET, P., MARTÍNEZ, S. and SAN MARTÍN, J. (1995). Asymptotic laws for onedimensional diffusions conditioned to nonabsorption. Ann. Probab. 23 1300-1314.
    • (1995) Ann. Probab. , vol.23 , pp. 1300-1314
    • Collet, P.1    Martínez, S.2    San Martín, J.3
  • 4
    • 0004252602 scopus 로고
    • 2nd ed. Graduate Texts in Mathematics. Springer, New York
    • CONWAY, J. B. (1990). A Course in Functional Analysis, 2nd ed. Graduate Texts in Mathematics 96. Springer, New York.
    • (1990) A Course in Functional Analysis , vol.96
    • Conway, J.B.1
  • 5
    • 0000381122 scopus 로고
    • Quasi-stationary distributions and convergence to quasistationarity of birth-death processes
    • VAN DOORN, E. A. (1991). Quasi-stationary distributions and convergence to quasistationarity of birth-death processes. Adv. in Appl. Probab. 23 683-700.
    • (1991) Adv. in Appl. Probab. , vol.23 , pp. 683-700
    • Van Doorn, E.A.1
  • 6
    • 21244443116 scopus 로고    scopus 로고
    • Survival and extinction in a locally regulated population
    • ETHERIDGE, A. M. (2004). Survival and extinction in a locally regulated population. Ann. Appl. Probab. 14 188-214.
    • (2004) Ann. Appl. Probab. , vol.14 , pp. 188-214
    • Etheridge, A.M.1
  • 7
    • 0001240798 scopus 로고
    • Existence of quasistationary distributions. A renewal dynamical approach
    • FERRARI, P. A., KESTEN, H., MARTINEZ, S. and PICCO, P. (1995). Existence of quasistationary distributions. A renewal dynamical approach. Ann. Probab. 23 501-521.
    • (1995) Ann. Probab. , vol.23 , pp. 501-521
    • Ferrari, P.A.1    Kesten, H.2    Martinez, S.3    Picco, P.4
  • 10
    • 0035593503 scopus 로고    scopus 로고
    • Asymptotic behavior of absorbing Markov chains conditional on nonabsorption for applications in conservation biology
    • GOSSELIN, F. (2001). Asymptotic behavior of absorbing Markov chains conditional on nonabsorption for applications in conservation biology. Ann. Appl. Probab. 11 261-284.
    • (2001) Ann. Appl. Probab. , vol.11 , pp. 261-284
    • Gosselin, F.1
  • 13
    • 0002639718 scopus 로고
    • Weak convergence of sequences of semimartingales with applications to multitype branching processes
    • JOFFE, A. and MÉTIVIER, M. (1986). Weak convergence of sequences of semimartingales with applications to multitype branching processes. Adv. in Appl. Probab. 18 20-65.
    • (1986) Adv. in Appl. Probab. , vol.18 , pp. 20-65
    • Joffe, A.1    Métivier, M.2
  • 17
    • 0002851231 scopus 로고
    • A certain property of solutions of parabolic equations with measurable coefficients
    • KRYLOV, N. and SAFONOV, M. (1981). A certain property of solutions of parabolic equations with measurable coefficients. Math. USSR-Izv. 16 151-164.
    • (1981) Math. USSR-Izv. , vol.16 , pp. 151-164
    • Krylov, N.1    Safonov, M.2
  • 18
    • 21244454922 scopus 로고    scopus 로고
    • The branching process with logistic growth
    • LAMBERT, A. (2005). The branching process with logistic growth. Ann. Appl. Probab. 15 1506-1535.
    • (2005) Ann. Appl. Probab. , vol.15 , pp. 1506-1535
    • Lambert, A.1
  • 19
    • 34147104061 scopus 로고    scopus 로고
    • Quasi-stationary distributions and the continuous-state branching process conditioned to be never extinct
    • (electronic)
    • LAMBERT, A. (2007). Quasi-stationary distributions and the continuous-state branching process conditioned to be never extinct. Electron. J. Probab. 12 420-446 (electronic).
    • (2007) Electron. J. Probab. , vol.12 , pp. 420-446
    • Lambert, A.1
  • 20
    • 55849151351 scopus 로고    scopus 로고
    • Population dynamics and random genealogies
    • LAMBERT, A. (2008). Population dynamics and random genealogies. Stoch. Models 24 45-163.
    • (2008) Stoch. Models , vol.24 , pp. 45-163
    • Lambert, A.1
  • 21
    • 34548008453 scopus 로고
    • Limiting diffusions for population-size dependent branching processes
    • LIPOW, C. (1977). Limiting diffusions for population-size dependent branching processes. J. Appl. Probab. 14 14-24.
    • (1977) J. Appl. Probab. , vol.14 , pp. 14-24
    • Lipow, C.1
  • 22
    • 0001443492 scopus 로고
    • Spectral theory of semigroups connected with diffusion processes and its application
    • MANDL, P. (1961). Spectral theory of semigroups connected with diffusion processes and its application. Czech. Math. J. 11 558-569.
    • (1961) Czech. Math. J. , vol.11 , pp. 558-569
    • Mandl, P.1
  • 23
    • 17144468382 scopus 로고    scopus 로고
    • Classification of killed one-dimensional diffusions
    • MARTÍNEZ, S. and SAN MARTÍN, J. (2004). Classification of killed one-dimensional diffusions. Ann. Probab. 32 530-552.
    • (2004) Ann. Probab. , vol.32 , pp. 530-552
    • Martínez, S.1    San Martín, J.2
  • 24
    • 77149155164 scopus 로고    scopus 로고
    • Quasi-stationary distributions: A bibliography. Available at, regularly updated
    • POLLETT, P. K. (2008). Quasi-stationary distributions: A bibliography. Available at http://www.maths.uq.edu.au/~pkp/papers/qsds/qsds.html, regularly updated.
    • (2008)
    • Pollett, P.K.1
  • 28
    • 0000564723 scopus 로고
    • On quasi-stationary distributions in discretetime Markov chains with a denumerable infinity of states
    • SENETA, E. and VERE-JONES, D. (1966). On quasi-stationary distributions in discretetime 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    Vere-Jones, D.2
  • 29
    • 2442581375 scopus 로고    scopus 로고
    • Markov mortality models: Implications of quasistationarity and varying initial distributions
    • STEINSALTZ, D. and EVANS, S. N. (2004). Markov mortality models: Implications of quasistationarity and varying initial distributions. Theor. Pop. Biol. 65 319-337.
    • (2004) Theor. Pop. Biol. , vol.65 , pp. 319-337
    • Steinsaltz, D.1    Evans, S.N.2
  • 30
    • 38949165926 scopus 로고    scopus 로고
    • Quasistationary distributions for one-dimensional diffusions with killing
    • (electronic)
    • STEINSALTZ, D. and EVANS, S. N. (2007). Quasistationary distributions for one-dimensional diffusions with killing. Trans. Amer. Math. Soc. 359 1285-1324 (electronic).
    • (2007) Trans. Amer. Math. Soc. , vol.359 , pp. 1285-1324
    • Steinsaltz, D.1    Evans, S.N.2
  • 31
    • 84981749879 scopus 로고
    • Pointwise estimates and quasilinear parabolic equations
    • TRUDINGER, N. S. (1968). Pointwise estimates and quasilinear parabolic equations. Comm. Pure Appl. Math. 21 205-226.
    • (1968) Comm. Pure Appl. Math. , vol.21 , pp. 205-226
    • Trudinger, N.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.