Birth-death processes with killing

Statistics and Probability Letters

Volumn 72, Issue 1, 2005, Pages 33-42

  van Doorn, Erik A ^a   Zeifman, Alexander I ^b  

^a UNIVERSITY OF TWENTE   (Netherlands)

^b VOLOGDA STATE UNIVERSITY   (Russian Federation)

Author keywords

Karlin McGregor representation; Orthogonal polynomials; State dependent killing rate; Total catastrophe; Transition function; Transition probabilities

Indexed keywords

EID: 14644429782     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2004.11.020     Document Type: Article

References (9)

1. W.J. Anderson Continuous-Time Markov Chains 1991 Springer New York
2. X. Chao Y. Zheng Transient analysis of immigration birth-death processes with total catastrophes Probab. Engrg. Inform. Sci. 17 2003 83-106
3. T.S. Chihara An Introduction to Orthogonal Polynomials 1978 Gordon and Breach New York
4. E.A. van Doorn The indeterminate rate problem for birth-death processes Pacific J. Math. 130 1987 379-393
5. van Doorn, E.A., Zeifman, A.I., 2005. Extinction probability in a birth-death process with killing. J. Appl. Probab. 42, to appear.
6. S. Karlin J.L. McGregor The differential equations of birth-and-death processes, and the Stieltjes moment problem Trans. Amer. Math. Soc. 85 1957 589-646
7. S. Karlin J.L. McGregor A characterization of birth and death processes Proc. Natl. Acad. Sci. USA 45 1959 375-379
8. S. Karlin S. Tavaré Linear birth and death processes with killing J. Appl. Probab. 19 1982 477-487
9. R.B. Lenin P.R. Parthasarathy W.R.W. Scheinhardt E.A. van Doorn Families of birth-death processes with similar time-dependent behaviour J. Appl. Probab. 37 2000 835-849