The Reuter-Ledermann representation for birth and death processes
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- by Edward C. Waymire PDF
- Proc. Amer. Math. Soc. 57 (1976), 318-320 Request permission
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
- Patrick Billingsley, Convergence of probability measures, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0233396
- W. Ledermann and G. E. H. Reuter, Spectral theory for the differential equations of simple birth and death processes, Philos. Trans. Roy. Soc. London Ser. A 246 (1954), 321–369. MR 60103, DOI 10.1098/rsta.1954.0001
- 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 91566, DOI 10.1090/S0002-9947-1957-0091566-1
- Samuel Karlin and James McGregor, The classification of birth and death processes, Trans. Amer. Math. Soc. 86 (1957), 366–400. MR 94854, DOI 10.1090/S0002-9947-1957-0094854-8
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 57 (1976), 318-320
- MSC: Primary 60J80
- DOI: https://doi.org/10.1090/S0002-9939-1976-0420898-7
- MathSciNet review: 0420898