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Volumn 44, Issue 2, 2007, Pages 476-491

Computable bounds for the decay parameter of a birth-death process

Author keywords

Approximation; Exponential ergodicity; Quasi stationary distribution

Indexed keywords


EID: 34548038623     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1183667415     Document Type: Article
Times cited : (10)

References (30)
  • 2
    • 0001566894 scopus 로고
    • Application of Stieltjes theory for S-fractions to birth and death processes
    • BORDES, G. AND ROEHNER, B. (1983). Application of Stieltjes theory for S-fractions to birth and death processes. Adv. Appl. Prob. 15, 507-530.
    • (1983) Adv. Appl. Prob , vol.15 , pp. 507-530
    • BORDES, G.1    ROEHNER, B.2
  • 3
    • 0034701978 scopus 로고    scopus 로고
    • Approximations of quasi-stationary distributions for Markov chains
    • BREYER, L. A. AND HART, A. G. (2000), Approximations of quasi-stationary distributions for Markov chains. Math. Comput. Modelling 31, 69-79.
    • (2000) Math. Comput. Modelling , vol.31 , pp. 69-79
    • BREYER, L.A.1    HART, A.G.2
  • 4
    • 11244343202 scopus 로고
    • On exponential ergodicity and spectral structure for birth-death processes. I
    • CALLAERT, H. AND KEILSON, J. (1973). On exponential ergodicity and spectral structure for birth-death processes. I. Stoch. Process. Appl. 1, 187-216.
    • (1973) Stoch. Process. Appl , vol.1 , pp. 187-216
    • CALLAERT, H.1    KEILSON, J.2
  • 5
    • 11244320782 scopus 로고
    • On exponential ergodicity and spectral structure for birth-death processes. II
    • CALLAERT, H. AND KEILSON, J. (1973). On exponential ergodicity and spectral structure for birth-death processes. II. Stoch. Process. Appl. 1, 217-235.
    • (1973) Stoch. Process. Appl , vol.1 , pp. 217-235
    • CALLAERT, H.1    KEILSON, J.2
  • 7
    • 0000699604 scopus 로고    scopus 로고
    • Estimation of spectral gap for Markov chains
    • CHEN, M.-F. (1996). Estimation of spectral gap for Markov chains. Acta. Math. Sinica New Ser. 12, 337-360.
    • (1996) Acta. Math. Sinica New Ser , vol.12 , pp. 337-360
    • CHEN, M.-F.1
  • 8
    • 0004828917 scopus 로고    scopus 로고
    • Explicit bounds of the first eigenvalue
    • CHEN, M.-F. (2000). Explicit bounds of the first eigenvalue. Sci. China Ser. A 43, 1051-1059.
    • (2000) Sci. China Ser. A , vol.43 , pp. 1051-1059
    • CHEN, M.-F.1
  • 9
    • 52549104564 scopus 로고    scopus 로고
    • Variational formulas and approximation theorems for the first eigenvalue in dimension one
    • CHEN, M.-F. (2001). Variational formulas and approximation theorems for the first eigenvalue in dimension one. Sci. China Ser. A 44, 409-418.
    • (2001) Sci. China Ser. A , vol.44 , pp. 409-418
    • CHEN, M.-F.1
  • 11
    • 0001383449 scopus 로고
    • On quasi-stationary distributions in absorbing continuous-time finite Markov chains
    • DARROCH, J. N. AND SENETA, E. (1967). On quasi-stationary distributions in absorbing continuous-time finite Markov chains. J. Appl. Prob. 4, 192-196.
    • (1967) J. Appl. Prob , vol.4 , pp. 192-196
    • DARROCH, J.N.1    SENETA, E.2
  • 12
    • 18444402697 scopus 로고
    • The limiting behavior of transient birth and death processes conditioned on survival
    • GOOD, P. (1968). The limiting behavior of transient birth and death processes conditioned on survival. J. Austral. Math. Soc. 8, 716-722.
    • (1968) J. Austral. Math. Soc , vol.8 , pp. 716-722
    • GOOD, P.1
  • 13
    • 34548019314 scopus 로고    scopus 로고
    • Calculation of the spectral ergodicity exponent for the birth and death process
    • KARTASHOV, N. V. (2000). Calculation of the spectral ergodicity exponent for the birth and death process. Ukrainian Math. J. 52, 1018-1028.
    • (2000) Ukrainian Math. J , vol.52 , pp. 1018-1028
    • KARTASHOV, N.V.1
  • 14
    • 21144472761 scopus 로고
    • Evaluation of the decay parameter for some specialized birth-death processes
    • KIJIMA, M. (1992). Evaluation of the decay parameter for some specialized birth-death processes, J. Appl. Prob. 29, 781-791.
    • (1992) J. Appl. Prob , vol.29 , pp. 781-791
    • KIJIMA, M.1
  • 15
    • 84960569835 scopus 로고
    • The exponential decay of Markov transition probabilities
    • KINGMAN, J. F. C. (1963), The exponential decay of Markov transition probabilities. Proc. London Math. Soc. (3) 13, 337-358.
    • (1963) Proc. London Math. Soc. (3) , vol.13 , pp. 337-358
    • KINGMAN, J.F.C.1
  • 16
    • 33750606874 scopus 로고    scopus 로고
    • Convergence rates in strong ergodicity for Markov processes
    • MAO, Y.-H. (2006). Convergence rates in strong ergodicity for Markov processes. Stoch. Process. Appl. 116, 1964-1976.
    • (2006) Stoch. Process. Appl , vol.116 , pp. 1964-1976
    • MAO, Y.-H.1
  • 17
    • 0000635179 scopus 로고    scopus 로고
    • The quasi-stationary distribution of the closed endemic SIS model
    • NÅSELL, I. (1996). The quasi-stationary distribution of the closed endemic SIS model. Adv. Appl. Prob. 28, 895-932.
    • (1996) Adv. Appl. Prob , vol.28 , pp. 895-932
    • NÅSELL, I.1
  • 18
    • 2542509066 scopus 로고    scopus 로고
    • On the quasi-stationary distribution of the stochastic logistic epidemic
    • NÅSELL, I. (1999). On the quasi-stationary distribution of the stochastic logistic epidemic, Math. Biosci. 156, 21-40.
    • (1999) Math. Biosci , vol.156 , pp. 21-40
    • NÅSELL, I.1
  • 19
    • 0035822368 scopus 로고    scopus 로고
    • Extinction and quasi-stationarity in the Verhulst logistic model
    • NÅSELL, I. (2001). Extinction and quasi-stationarity in the Verhulst logistic model. J. Theoret. Biol. 211, 11-27.
    • (2001) J. Theoret. Biol , vol.211 , pp. 11-27
    • NÅSELL, I.1
  • 20
    • 0013675615 scopus 로고
    • The determination of quasistationary distributions directly from the transition rates of an absorbing Markov chain
    • POLLETT, P. K. (1995). The determination of quasistationary distributions directly from the transition rates of an absorbing Markov chain. Math. Comput. Modelling 22, 279-287.
    • (1995) Math. Comput. Modelling , vol.22 , pp. 279-287
    • POLLETT, P.K.1
  • 21
    • 0002855907 scopus 로고
    • Denumerable Markov processes and the associated contraction semigroups on l
    • REUTER, G. E. H. (1957). Denumerable Markov processes and the associated contraction semigroups on l. Acta Math. 97, 1-46.
    • (1957) Acta Math , vol.97 , pp. 1-46
    • REUTER, G.E.H.1
  • 22
    • 0020194952 scopus 로고
    • Solving the birth and death processes with quadratic asymptotically symmetric transition rates
    • ROEHNER, B. AND VALENT, G. (1982). Solving the birth and death processes with quadratic asymptotically symmetric transition rates. SIAM J. Appl. Math. 42, 1020-1046.
    • (1982) SIAM J. Appl. Math , vol.42 , pp. 1020-1046
    • ROEHNER, B.1    VALENT, G.2
  • 23
    • 0003046508 scopus 로고
    • Quasi-stationary behaviour in the random walk with continuous time
    • SENETA, E. (1966). Quasi-stationary behaviour in the random walk with continuous time. Austral. J. Statist. 8, 92-98.
    • (1966) Austral. J. Statist , vol.8 , pp. 92-98
    • SENETA, E.1
  • 24
    • 0013437873 scopus 로고
    • Criteria for ergodicity, exponential ergodicity and strong ergodicity of Markov processes
    • TWEEDIE, R. L. (1981). Criteria for ergodicity, exponential ergodicity and strong ergodicity of Markov processes. J. Appl. Prob. 18, 122-130.
    • (1981) J. Appl. Prob , vol.18 , pp. 122-130
    • TWEEDIE, R.L.1
  • 25
    • 0000783136 scopus 로고
    • Conditions for exponential ergodicity and bounds for the decay parameter of a birth-death process
    • VAN DOORN, E. A. (1985). Conditions for exponential ergodicity and bounds for the decay parameter of a birth-death process. Adv. Appl. Prob. 17, 514-530.
    • (1985) Adv. Appl. Prob , vol.17 , pp. 514-530
    • VAN DOORN, E.A.1
  • 26
    • 0000381122 scopus 로고
    • Quasi-stationary distributions and convergence to quasi-stationarity of birth-death processes
    • VAN DOORN, E. A. (1991). Quasi-stationary distributions and convergence to quasi-stationarity of birth-death processes. Adv. Appl. Prob. 23, 683-700.
    • (1991) Adv. Appl. Prob , vol.23 , pp. 683-700
    • VAN DOORN, E.A.1
  • 27
    • 0038313575 scopus 로고    scopus 로고
    • Representations for the rate of convergence of birth-death processes
    • VAN DOORN, E. A. (2002). Representations for the rate of convergence of birth-death processes. Theory Prob. Math. Statist. 65, 37-43.
    • (2002) Theory Prob. Math. Statist , vol.65 , pp. 37-43
    • VAN DOORN, E.A.1
  • 28
    • 0000161729 scopus 로고
    • Conditioned Markov processes
    • WAUGH, W. A. O'N. (1958). Conditioned Markov processes. Biometrika 45, 241-249.
    • (1958) Biometrika , vol.45 , pp. 241-249
    • WAUGH, W.1    O'N, A.2
  • 29
    • 0001800918 scopus 로고
    • Some estimates of the rate of convergence for birth and death processes
    • ZEǏFMAN, A. I. (1991). Some estimates of the rate of convergence for birth and death processes. J. Appl. Prob. 28, 268-277.
    • (1991) J. Appl. Prob , vol.28 , pp. 268-277
    • ZEǏFMAN, A.I.1
  • 30
    • 0041908471 scopus 로고    scopus 로고
    • Strong ergodicity of monotone transition functions
    • ZHANG, H., CHEN, A., LIN, X. AND HOU, Z. (2001). Strong ergodicity of monotone transition functions. Statist. Prob. Lett. 55, 63-69.
    • (2001) Statist. Prob. Lett , vol.55 , pp. 63-69
    • ZHANG, H.1    CHEN, A.2    LIN, X.3    HOU, Z.4


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