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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2010/784567 |
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| _version_ | 1849407800062509056 |
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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. |
| format | Article |
| id | doaj-art-43b0fc99d105461984a4793bb89bc71d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| 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 |