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The Reuter-Ledermann representation for birth and death processes

Author: Edward C. Waymire
Journal: Proc. Amer. Math. Soc. 57 (1976), 318-320
MSC: Primary 60J80
MathSciNet review: 0420898
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Abstract: The identification of the mass of the integrator at zero is made for the integral representation obtained by Reuter and Ledermann for the transition probabilities of birth and death processes. An ergodic theorem is given as an application of this result.

References [Enhancements On Off] (What's this?)

  • [1] P. Billingsley (1968), Convergence of probability measures, Wiley, New York. MR 38 #1718. MR 0233396 (38:1718)
  • [2] W. Ledermann and G. E. H. Reuter (1954), Spectral theory for the differential equations of simple birth and death processes, Philos. Trans. Roy. Soc. London Ser. A 246, 321-369. MR 15, 625. MR 0060103 (15:625g)
  • [3] S. Karlin, and J. L. McGregor (1957a), The differential equation of birth-and-death processes, and the Stieltjes moment problem, Trans. Amer. Math. Soc. 85, 489-546. MR 19, 989. MR 0091566 (19:989d)
  • [4] -(1956b), The classification of birth and death processes, Trans. Amer. Math. Soc. 86, 366-400. MR 20 # 1363. MR 0094854 (20:1363)

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