Integrals for continuous-time Markov chains

Mathematical Biosciences

Volumn 182, Issue 2, 2003, Pages 213-225

  Pollett, P K ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

Birth death processes; Catastrophe processes; Hitting times; Path integrals; Potential theory

Indexed keywords

INTEGRATION; MATHEMATICAL MODELS;

CATASTROPHE PROCESS;

MARKOV PROCESSES;

MARKOV CHAIN;

ANALYTIC METHOD; ARTICLE; BIRTH; DEATH; DISASTER; PROBABILITY;

BIRTH RATE; COMPUTER SIMULATION; DISASTERS; EPIDEMIOLOGIC METHODS; MARKOV CHAINS; MORTALITY; POISSON DISTRIBUTION; TIME FACTORS;

EID: 0037376826     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0025-5564(02)00161-X     Document Type: Article

References (10)

1. V.T. Stefanov, S. Wang, A note on integrals for birth-death processes, Math. Biosci. 168 (2000) 161.
2. C.M. Hernández-Suárez, C. Castillo-Chavez, A basic result on the integral for birth-death Markov processes, Math. Biosci. 161 (1999) 95.
3. W.J. Anderson, Continuous-Time Markov Chains: An Applications-Oriented Approach, Springer, New York, 1991.
4. J.R. Norris, Markov Chains, Cambridge University, Cambridge, 1997.
5. M. Mangel, C. Tier, Four facts every conservation biologist should know about persistence, Ecology 75 (1994) 607.
6. D.R. McNeil, Integral functionals of birth and death processes and related limiting distributions, Ann. Math. Statist. 41 (1970) 480.
7. W. Ledermann, G.E.H. Reuter, Spectral theory for the differential equations of simple birth and death processes, Philos. Trans. R. Soc. London 246 (1954) 321.
8. P.K. Pollett, Quasi-stationarity in populations that are subject to large-scale mortality or emigration, Environ. Int. 27 (2001) 231.
9. P.J. Brockwell, The extinction time of a birth, death and catastrophe process and of a related diffusion model, Adv. Appl. Probab. 17 (1985) 42.
10. T.H. Harris, The Theory of Branching Processes, Springer, Berlin, 1963.