Conditional Processes Induced by Birth and Death Processes

For birth and death processes with finite state space, we consider stochastic processes induced by conditioning on hitting the right boundary point before hitting the left boundary point. We call the induced stochastic processes the conditional processes. We show that the conditional processes are a...

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Main Authors: Masaru Iizuka, Matsuyo Tomisaki
Format: Article
Language:English
Published: Wiley 2010-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2010/784567
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author Masaru Iizuka
Matsuyo Tomisaki
author_facet Masaru Iizuka
Matsuyo Tomisaki
author_sort Masaru Iizuka
collection DOAJ
description For birth and death processes with finite state space, we consider stochastic processes induced by conditioning on hitting the right boundary point before hitting the left boundary point. We call the induced stochastic processes the conditional processes. We show that the conditional processes are again birth and death processes when the right boundary point is absorbing. On the other hand, it is shown that the conditional processes do not have Markov property and they are not birth and death processes when the right boundary point is reflecting.
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institution Kabale University
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spelling doaj-art-43b0fc99d105461984a4793bb89bc71d2025-08-20T03:35:57ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/784567784567Conditional Processes Induced by Birth and Death ProcessesMasaru Iizuka0Matsuyo Tomisaki1Division of Mathematics, Kyushu Dental College, 2-6-1 Manazuru, Kokurakita-ku, Kitakyushu 803-8580, JapanDepartment of Mathematics, Faculty of Science, Nara Women's University, Kita-Uoya Nishimachi, Nara 630-8506, JapanFor birth and death processes with finite state space, we consider stochastic processes induced by conditioning on hitting the right boundary point before hitting the left boundary point. We call the induced stochastic processes the conditional processes. We show that the conditional processes are again birth and death processes when the right boundary point is absorbing. On the other hand, it is shown that the conditional processes do not have Markov property and they are not birth and death processes when the right boundary point is reflecting.http://dx.doi.org/10.1155/2010/784567
spellingShingle Masaru Iizuka
Matsuyo Tomisaki
Conditional Processes Induced by Birth and Death Processes
International Journal of Mathematics and Mathematical Sciences
title Conditional Processes Induced by Birth and Death Processes
title_full Conditional Processes Induced by Birth and Death Processes
title_fullStr Conditional Processes Induced by Birth and Death Processes
title_full_unstemmed Conditional Processes Induced by Birth and Death Processes
title_short Conditional Processes Induced by Birth and Death Processes
title_sort conditional processes induced by birth and death processes
url http://dx.doi.org/10.1155/2010/784567
work_keys_str_mv AT masaruiizuka conditionalprocessesinducedbybirthanddeathprocesses
AT matsuyotomisaki conditionalprocessesinducedbybirthanddeathprocesses