Geodesic
Pathological Birth-and-Death Processes and the Spectral Theory of Strings
Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 2, pp. 74-78.

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In a 1957 paper, Karlin and McGregor discovered the existence of birth-and-death processes for which the Chapman–Kolmogorov equation does not hold. Such processes are said to be pathological. We disclose the probability nature of pathological birth-and-death processes with the help of M. Krein's spectral theory of strings.
Keywords: birth-and-death process, string, spectral theory, generalized diffusion process. 
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I. S. Kats. Pathological Birth-and-Death Processes and the Spectral Theory of Strings. Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 2, pp. 74-78. http://geodesic.mathdoc.fr/item/FAA_2005_39_2_a7/

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