The classification of birth and death processes

Authors:
Samuel Karlin and James McGregor

Journal:
Trans. Amer. Math. Soc. **86** (1957), 366-400

MSC:
Primary 60.00; Secondary 34.00

DOI:
https://doi.org/10.1090/S0002-9947-1957-0094854-8

MathSciNet review:
0094854

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References | Similar Articles | Additional Information

**[1]**S. Karlin and J. L. McGregor,*The differential equations of birth-and-death processes, and the Stieltjes moment problem*, Trans. Amer. Math. Soc.**85**(1957), 489–546. MR**0091566**, https://doi.org/10.1090/S0002-9947-1957-0091566-1**[2]**K. L. Chung,*Foundations of the theory of continuous parameter Markov chains*, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, vol. II, University of California Press, Berkeley and Los Angeles, 1956, pp. 29–40. MR**0084884****[3]**F. G. Foster,*On the stochastic matrices associated with certain queuing processes*, Ann. Math. Statistics**24**(1953), 355–360. MR**0056232****[4]**Richard Bellman and Theodore Harris,*Recurrence times for the Ehrenfest model*, Pacific J. Math.**1**(1951), 179–193. MR**0045323****[5]**T. E. Harris,*First passage and recurrence distributions*, Trans. Amer. Math. Soc.**73**(1952), 471–486. MR**0052057**, https://doi.org/10.1090/S0002-9947-1952-0052057-2**[6]**David G. Kendall,*On the generalized “birth-and-death” process*, Ann. Math. Statistics**19**(1948), 1–15. MR**0024091****[7]**J. A. Shohat and J. D. Tamarkin,*The Problem of Moments*, American Mathematical Society Mathematical surveys, vol. I, American Mathematical Society, New York, 1943. MR**0008438****[8]**E. C. Titchmarsh,*Introduction to the theory of Fourier integrals*, Oxford, 1948.**[9]**C. Derman,*A solution to a set of fundamental equations in Markov chains*, Proc. Amer. Math. Soc.**5**(1954), 332–334. MR**0060757**, https://doi.org/10.1090/S0002-9939-1954-0060757-0

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DOI:
https://doi.org/10.1090/S0002-9947-1957-0094854-8

Article copyright:
© Copyright 1957
American Mathematical Society