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Funktsional'nyi Analiz i ego Prilozheniya, 2005, Volume 39, Issue 2, Pages 74–78
DOI: https://doi.org/10.4213/faa43 (Mi faa43) 		 
This article is cited in 3 scientific papers (total 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
Full-text PDF (198 kB) Citations (3)
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DOI: https://doi.org/10.4213/faa43
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.
Received: 24.07.2003
English version:
Functional Analysis and Its Applications, 2005, Volume 39, Issue 2, Pages 144–147
DOI: https://doi.org/10.1007/s10688-005-0028-2
Bibliographic databases:
Document Type: Article
UDC: 517.9+519.21
Language: Russian
Citation: I. S. Kats, “Pathological Birth-and-Death Processes and the Spectral Theory of Strings”, Funktsional. Anal. i Prilozhen., 39:2 (2005), 74–78; Funct. Anal. Appl., 39:2 (2005), 144–147
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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