Birth-death processes and associated polynomials

Journal of Computational and Applied Mathematics

Volumn 153, Issue 1-2, 2003, Pages 497-506

  van Doorn, Erik A ^a  

^a UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

recurrence; First entrance time; Orthogonal polynomials; Recurrence; Spectral measure

Indexed keywords

INTEGER PROGRAMMING; POLYNOMIALS; PROBABILITY;

BIRTH-DEATH PROCESSES;

COMPUTATIONAL METHODS;

MATHEMATICAL ANALYSIS;

EID: 0037382222     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(02)00594-0     Document Type: Article

References (19)

1. J. Abate, W. Whitt, Simple spectral representations for the M/M/1 queue. Queueing Systems Theory Appl. 3 (1988) 321-346.
2. W.J. Anderson, Continuous-Time Markov Chains, Apringer, New York, 1991.
3. C. Berg, Markov's theorem revisited. J. Approx. Theory 78 (1994) 260-275.
4. H. Callaert, On the rate of convergence in birth-and-death processes. Bull. Soc. Math. Belg. 26 (1974) 173-184.
5. T.S. Chihara, An Introduction to Orthogonal Polynomials, Gordon & Breach, New York, 1978.
6. T.S. Chihara, Indeterminate symmetric moment problems. J. Math. Anal. Appl. 85 (1982) 331-346.
7. H. Dette, First return probabilities of birth and death chains and associated orthogonal polynomials. Proc. Amer. Math. Soc. 129 (2000) 1805-1815.
8. E.A. van Doorn, Conditions for exponential ergodicity and bounds for the decay parameter of a birth-death process. Adv. Appl. Probab. 17 (1985) 514-530.
9. E.A. van Doorn, On associated polynomials and decay rates for birth-death processes, submitted for publication.
10. M.E. Ismail, J. Letessier, G. Valent, Linear birth and death models and associated Laguerre and Meixner polynomials. J. Approx. Theory 55 (1988) 337-348.
11. 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.
12. S. Karlin, J.L. McGregor, The classification of birth and death processes. Trans. Amer. Math. Soc. 86 (1957) 366-400.
13. S. Karlin, J.L. McGregor, Many server queueing processes with Poisson input and exponential service times. Pacific J. Math. 8 (1958) 87-118.
14. S. Karlin, J.L. McGregor, Linear growth, birth and death processes. J. Math. Mech. 7 (1958) 643-662.
15. S. Karlin, J.L. McGregor, Random walks. Illinois J. Math. 3 (1959) 66-81.
16. R.B. Lenin, P.R. Parthasarathy, W.R. Scheinhardt, E.A. van Doorn, Families of birth-death processes with similar time-dependent behaviour. J. Appl. Probab. 37 (2000) 835-849.
17. J. Sherman, On the numerators of the convergents of the Stieltjes continued fractions. Trans. Amer. Math. Soc. 35 (1933) 64-87.
18. 2 - ..., Proc. Nat. Acad. Sci. U.S.A. 18 (1932) 283-287.
19. D.V. Widder, The Laplace Transform, Princeton University Press, London, 1946.