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Intertwining of birth-and-death processes
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SYSNO ASEP 0357433 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Intertwining of birth-and-death processes Author(s) Swart, Jan M. (UTIA-B) RID, ORCID Source Title Kybernetika. - : Ústav teorie informace a automatizace AV ČR, v. v. i. - ISSN 0023-5954
Roč. 47, č. 1 (2011), s. 1-14Number of pages 14 s. Publication form WWW - WWW Language eng - English Country CZ - Czech Republic Keywords Intertwining of Markov processes ; birth and death process ; averaged Markov process ; first passage time ; coupling ; eigenvalues Subject RIV BA - General Mathematics R&D Projects GA201/09/1931 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10750506 - UTIA-B (2005-2011) UT WOS 000288625300001 Annotation It has been known for a long time that for birth-and-death processes started in zero the first passage time of a given level is distributed as a sum of independent exponentially distributed random variables, the parameters of which are the negatives of the eigenvalues of the stopped process. Recently, Diaconis and Miclo have given a probabilistic proof of this fact by constructing a coupling between a general birth-and-death process and a process whose birth rates are the negatives of the eigenvalues, ordered from high to low, and whose death rates are zero, in such a way that the latter process is always ahead of the former, and both arrive at the same time at the given level. In this note, we extend their methods by constructing a third process, whose birth rates are the negatives of the eigenvalues ordered from low to high and whose death rates are zero, which always lags behind the original process and also arrives at the same time. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2011
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