INFINITE MARKOV PARTICLE SYSTEMS ASSOCIATED WITH ABSORBING STABLE MOTION ON A HALF SPACE

Hiraba, Seiji

doi:info:doi/10.18910/29201

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タイトル	INFINITE MARKOV PARTICLE SYSTEMS ASSOCIATED WITH ABSORBING STABLE MOTION ON A HALF SPACE
著者	Hiraba, Seiji Hiraba, Seiji
抄録	In general, for a Markov process which does not have an invariant measure, it is possible to realize a stationary Markov process with the same transition probability by extending the probability space and by adding new paths which are born at random times. The distribution (which may not be a probability measure) is called a Kuznetsov measure. By using this measure we can construct a stationary Markov particle system, which is called an equilibrium process with immigration. This particle system can be decomposed as a sum of the original part and the immigration part (see [2]). In the present paper, we consider an absorbing stable motion on a half space H, i.e., a time-changed absorbing Brownian motion on H by an increasing strictly stable process. We first give the martingale characterization of the particle system. Secondly, we discuss the finiteness of the number of particles near the boundary of the immigration part. (cf. [2], [3], [4].)
公開者	Osaka University and Osaka City University, Departments of Mathematics
掲載誌名	Osaka Journal of Mathematics
巻	51
号	2
開始ページ	337
終了ページ	358
刊行年月	2014-04
ISSN	00306126
NCID	AA00765910
URL	http://hdl.handle.net/11094/29201
言語	英語
DOI	info:doi/10.18910/29201

著者版フラグ	publisher
NII資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
dcmi資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics.51(2) P.337-P.358
DC.title	INFINITE MARKOV PARTICLE SYSTEMS ASSOCIATED WITH ABSORBING STABLE MOTION ON A HALF SPACE
DC.creator	Hiraba, Seiji
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language" scheme="DCTERMS.RFC1766	英語
DCTERMS.issued" scheme="DCTERMS.W3CDTF	2014-04
DC.identifier" scheme="DCTERMS.URI	http://hdl.handle.net/11094/29201
DCTERMS.abstract	In general, for a Markov process which does not have an invariant measure, it is possible to realize a stationary Markov process with the same transition probability by extending the probability space and by adding new paths which are born at random times. The distribution (which may not be a probability measure) is called a Kuznetsov measure. By using this measure we can construct a stationary Markov particle system, which is called an equilibrium process with immigration. This particle system can be decomposed as a sum of the original part and the immigration part (see [2]). In the present paper, we consider an absorbing stable motion on a half space H, i.e., a time-changed absorbing Brownian motion on H by an increasing strictly stable process. We first give the martingale characterization of the particle system. Secondly, we discuss the finiteness of the number of particles near the boundary of the immigration part. (cf. [2], [3], [4].)
DC.identifier	info:doi/10.18910/29201
citation_title	INFINITE MARKOV PARTICLE SYSTEMS ASSOCIATED WITH ABSORBING STABLE MOTION ON A HALF SPACE
citation_author	Hiraba, Seiji
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2014-04
citation_journal_title	Osaka Journal of Mathematics
citation_volume	51
citation_issue	2
citation_firstpage	337
citation_lastpage	358
citation_issn	00306126
citation_public_url	http://hdl.handle.net/11094/29201
citation_doi	info:doi/10.18910/29201

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