Potential Theory and Right Processes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2004
|
| Schriftenreihe: | Mathematics and Its Applications
572 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The developmentsin the recent yearsof the potential theoryemphasized a classof functions larger than that of excessive functions (i.e. the positive superharmonic functionsfromtheclassicalpotentialtheoryassociatedwiththeLaplaceoperator), namely the strongly supermedian functions. It turns out that a positive Borel function will be strongly supermedian if and only if it is the in?mum of all its excessive majorants. Apparently, these functions have been introduced by J.F. Mertens and then they have been studied mainly by P.A. Meyer, G. Mokobodzki, D. Feyel and recently by P.J. Fitzsimmons and R.K. Getoor. The aimofthis bookisamongothersto developa potential theoryappropriate to this new class of functions. Although our methods are analytical, we present also the probabilistic counterparts from the Markov processes theory. The natural frame in which this theory is settled is given by a sub-Markovian resolvent of kernels on a Radon measurable space. After a possible extension of the space, such a resolvent becomes that one associated with a right process on a Radon topological space, not necessary locally compact and without existing a reference measure. Intimately related to the excessive functions we present certain basic tools of the theory: the Ray topology and compacti?cation, the ?ne carrier and the reduction operation on measurable sets. We examine di?erent types of negligible sets with respect to a ?nite measure ?:the ?-polar, ?-semipolar and ?-mince sets. We take advantage of the cone of potentials structure for both excessive functions and measures |
| Beschreibung: | 1 Online-Ressource (VI, 370 p) |
| ISBN: | 9781402024979 9789048166718 |
| DOI: | 10.1007/978-1-4020-2497-9 |
Internformat
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| 500 | |a The developmentsin the recent yearsof the potential theoryemphasized a classof functions larger than that of excessive functions (i.e. the positive superharmonic functionsfromtheclassicalpotentialtheoryassociatedwiththeLaplaceoperator), namely the strongly supermedian functions. It turns out that a positive Borel function will be strongly supermedian if and only if it is the in?mum of all its excessive majorants. Apparently, these functions have been introduced by J.F. Mertens and then they have been studied mainly by P.A. Meyer, G. Mokobodzki, D. Feyel and recently by P.J. Fitzsimmons and R.K. Getoor. The aimofthis bookisamongothersto developa potential theoryappropriate to this new class of functions. Although our methods are analytical, we present also the probabilistic counterparts from the Markov processes theory. The natural frame in which this theory is settled is given by a sub-Markovian resolvent of kernels on a Radon measurable space. After a possible extension of the space, such a resolvent becomes that one associated with a right process on a Radon topological space, not necessary locally compact and without existing a reference measure. Intimately related to the excessive functions we present certain basic tools of the theory: the Ray topology and compacti?cation, the ?ne carrier and the reduction operation on measurable sets. We examine di?erent types of negligible sets with respect to a ?nite measure ?:the ?-polar, ?-semipolar and ?-mince sets. We take advantage of the cone of potentials structure for both excessive functions and measures | ||
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4020-2497-9 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9781402024979 9789048166718 |
| language | English |
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| spelling | Beznea, Lucian Verfasser aut Potential Theory and Right Processes by Lucian Beznea, Nicu Boboc Dordrecht Springer Netherlands 2004 1 Online-Ressource (VI, 370 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 572 The developmentsin the recent yearsof the potential theoryemphasized a classof functions larger than that of excessive functions (i.e. the positive superharmonic functionsfromtheclassicalpotentialtheoryassociatedwiththeLaplaceoperator), namely the strongly supermedian functions. It turns out that a positive Borel function will be strongly supermedian if and only if it is the in?mum of all its excessive majorants. Apparently, these functions have been introduced by J.F. Mertens and then they have been studied mainly by P.A. Meyer, G. Mokobodzki, D. Feyel and recently by P.J. Fitzsimmons and R.K. Getoor. The aimofthis bookisamongothersto developa potential theoryappropriate to this new class of functions. Although our methods are analytical, we present also the probabilistic counterparts from the Markov processes theory. The natural frame in which this theory is settled is given by a sub-Markovian resolvent of kernels on a Radon measurable space. After a possible extension of the space, such a resolvent becomes that one associated with a right process on a Radon topological space, not necessary locally compact and without existing a reference measure. Intimately related to the excessive functions we present certain basic tools of the theory: the Ray topology and compacti?cation, the ?ne carrier and the reduction operation on measurable sets. We examine di?erent types of negligible sets with respect to a ?nite measure ?:the ?-polar, ?-semipolar and ?-mince sets. We take advantage of the cone of potentials structure for both excessive functions and measures Mathematics Potential theory (Mathematics) Distribution (Probability theory) Potential Theory Probability Theory and Stochastic Processes Applications of Mathematics Mathematical and Computational Biology Mathematik Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Potenzialtheorie (DE-588)4046939-6 s 1\p DE-604 Boboc, Nicu Sonstige oth https://doi.org/10.1007/978-1-4020-2497-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Beznea, Lucian Potential Theory and Right Processes Mathematics Potential theory (Mathematics) Distribution (Probability theory) Potential Theory Probability Theory and Stochastic Processes Applications of Mathematics Mathematical and Computational Biology Mathematik Potenzialtheorie (DE-588)4046939-6 gnd |
| subject_GND | (DE-588)4046939-6 |
| title | Potential Theory and Right Processes |
| title_auth | Potential Theory and Right Processes |
| title_exact_search | Potential Theory and Right Processes |
| title_full | Potential Theory and Right Processes by Lucian Beznea, Nicu Boboc |
| title_fullStr | Potential Theory and Right Processes by Lucian Beznea, Nicu Boboc |
| title_full_unstemmed | Potential Theory and Right Processes by Lucian Beznea, Nicu Boboc |
| title_short | Potential Theory and Right Processes |
| title_sort | potential theory and right processes |
| topic | Mathematics Potential theory (Mathematics) Distribution (Probability theory) Potential Theory Probability Theory and Stochastic Processes Applications of Mathematics Mathematical and Computational Biology Mathematik Potenzialtheorie (DE-588)4046939-6 gnd |
| topic_facet | Mathematics Potential theory (Mathematics) Distribution (Probability theory) Potential Theory Probability Theory and Stochastic Processes Applications of Mathematics Mathematical and Computational Biology Mathematik Potenzialtheorie |
| url | https://doi.org/10.1007/978-1-4020-2497-9 |
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