Markov processes and positive semigroups on some classes of weighted continuous function spaces
In this paper we study strongly continuous positive semigroups on particular classes of weighted continuous function space on a locally compact Hausdorff space X having a countable base. In particular we characterize those positive semigroups which are the transition semigroups of suitable Markov pr...
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| Published in | Rendiconti del Circolo matematico di Palermo Vol. 57; no. 1; pp. 61 - 82 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer-Verlag
01.04.2008
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0009-725X 1973-4409 |
| DOI | 10.1007/s12215-008-0003-x |
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| Abstract | In this paper we study strongly continuous positive semigroups on particular classes of weighted continuous function space on a locally compact Hausdorff space
X
having a countable base.
In particular we characterize those positive semigroups which are the transition semigroups of suitable Markov processes. Some applications are also discussed.
Keywords
Positive semigroup, Markov transition function, Markov process, Weighted continuous function space, Degenerate second order differential operator
Mathematics Subject Classification (2000)
47D06, 47D07, 60J60 |
|---|---|
| AbstractList | In this paper we study strongly continuous positive semigroups on particular classes of weighted continuous function space on a locally compact Hausdorff space
X
having a countable base.
In particular we characterize those positive semigroups which are the transition semigroups of suitable Markov processes. Some applications are also discussed.
Keywords
Positive semigroup, Markov transition function, Markov process, Weighted continuous function space, Degenerate second order differential operator
Mathematics Subject Classification (2000)
47D06, 47D07, 60J60 |
| Author | Musceo, Graziana Altomare, Francesco |
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| Keywords | Markov Process Compact Hausdorff Space Order Differential Operator Countable Base Banach Lattice |
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| References | Feller (CR17) 1952; 55 CR2 CR3 Altomare, Carbone (CR4) 1997; 213 Arendt, Chernoff, Kato (CR6) 1982; 8 CR8 CR19 CR7 CR18 Altomare, Carbone (CR5) 2001; 5 CR9 CR16 CR15 CR14 CR13 CR12 CR11 CR21 Altomare, Attalienti (CR1) 2002; 42 Bony, Courrège, Priouret (CR10) 1968; 18 Sato, Ueno (CR20) 1965; 4 3_CR5 3_CR17 3_CR6 3_CR16 3_CR3 3_CR19 3_CR4 3_CR18 3_CR9 3_CR7 3_CR8 3_CR1 3_CR2 3_CR20 3_CR11 3_CR10 3_CR21 3_CR13 3_CR12 3_CR15 3_CR14 |
| References_xml | – ident: CR21 – ident: CR19 – volume: 213 start-page: 308 year: 1997 end-page: 333 ident: CR4 article-title: On some degenerate differential operators on weighted function spaces publication-title: J. Math. Anal. Appl. – ident: CR18 – ident: CR3 – ident: CR14 – ident: CR15 – ident: CR2 – ident: CR16 – ident: CR12 – volume: 55 start-page: 468 year: 1952 end-page: 519 ident: CR17 article-title: The parabolic differential equations and the associated semigroups of transformation publication-title: Ann. of Math. – ident: CR13 – volume: 4 start-page: 529 year: 1965 end-page: 605 ident: CR20 article-title: Multi-dimensional diffusion and the Markov process on the boundary publication-title: J. Math. Kyoto University – volume: 8 start-page: 167 year: 1982 end-page: 180 ident: CR6 article-title: A generalization of dissipativity and positive semigroups publication-title: J. Operator Theory – ident: CR11 – ident: CR9 – ident: CR7 – ident: CR8 – volume: 18 start-page: 369 year: 1968 end-page: 521 ident: CR10 article-title: Semi-Groupes de Feller sur une variété a bord Compacte et problèmes aux limites intégro-différentiels du second ordre donnant lieu au principe du maximum publication-title: Ann. Inst. Fourier, Grenoble – volume: 42 start-page: 193 year: 2002 end-page: 211 ident: CR1 article-title: Degenerate evolution equations in weighted continuous function spaces, Markov processes and the Black-Scholes equation-Part I publication-title: Result. Math. – volume: 5 start-page: 1 year: 2001 end-page: 167 ident: CR5 article-title: Markov processes and diffusion equations on unbounded intervals publication-title: Taiwanese J. Math. – ident: 3_CR17 doi: 10.2307/1969644 – ident: 3_CR21 – ident: 3_CR15 doi: 10.1007/978-3-662-00031-1 – ident: 3_CR14 doi: 10.1016/1385-7258(86)90023-5 – ident: 3_CR1 doi: 10.1007/BF03322850 – ident: 3_CR16 – ident: 3_CR4 doi: 10.1006/jmaa.1997.5540 – ident: 3_CR8 – ident: 3_CR12 – ident: 3_CR19 doi: 10.1007/978-1-4612-5561-1 – ident: 3_CR6 – ident: 3_CR13 – ident: 3_CR11 doi: 10.1007/978-94-009-6484-6 – ident: 3_CR3 – ident: 3_CR5 doi: 10.11650/twjm/1500574892 – ident: 3_CR20 doi: 10.1215/kjm/1250524605 – ident: 3_CR18 doi: 10.1007/978-1-4684-9358-0 – ident: 3_CR10 doi: 10.5802/aif.306 – ident: 3_CR2 doi: 10.1515/9783110884586 – ident: 3_CR9 – ident: 3_CR7 doi: 10.1007/BFb0074922 |
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| Title | Markov processes and positive semigroups on some classes of weighted continuous function spaces |
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