This article is cited in 3 papers

Brief communications

Pathological Birth-and-Death Processes and the Spectral Theory of Strings

I. S. Kats

Odessa State Academy of Food Technology

Abstract: 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.

UDC: 517.9+519.21

Received: 24.07.2003

DOI: 10.4213/faa43

 English version: Functional Analysis and Its Applications, 2005, 39:2, 144–147

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