About: Intertwining of birth-and-death processes

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	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. 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. (en)
Title	Intertwining of birth-and-death processes Intertwining of birth-and-death processes (en)
skos:prefLabel	Intertwining of birth-and-death processes Intertwining of birth-and-death processes (en)
skos:notation	RIV/67985556:_____/11:00357433!RIV11-GA0-67985556
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/09/1931), Z(AV0Z10750506)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Swart, Jan M.
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav teorie informace a automatizace AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	205532
http://linked.open...ai/riv/idVysledku	RIV/67985556:_____/11:00357433
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Intertwining of Markov processes; birth and death process; averaged Markov process; first passage time; coupling; eigenvalues (en)
http://linked.open.../riv/klicoveSlovo	Intertwining of Markov processes averaged Markov process birth and death process first passage time coupling eigenvalues
http://linked.open...odStatuVydavatele	CZ - Česká republika
http://linked.open...ontrolniKodProRIV	[B6456063439C]
http://linked.open...i/riv/nazevZdroje	Kybernetika
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Large interacting lattice systems: Gibbs states and phase transitions
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	47
http://linked.open...iv/tvurceVysledku	Swart, Jan M.
http://linked.open...ain/vavai/riv/wos	000288625300001
http://linked.open...n/vavai/riv/zamer	Pokročilé matematické metody získávání, zpracování a využití informací a znalostí ve složitých a nedeterministických systémech
issn	0023-5954
number of pages	14 (xsd:int)

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