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The developmentsin the recent yearsof the potential theoryemphasized a classof functions larger than that of excessive functions (i. e. the positive superharmonic functionsfromtheclassica… Meer...

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Potential Theory and Right Processes - nieuw boek

ISBN: 9789048166718

The developmentsin the recent yearsof the potential theoryemphasized a classof functions larger than that of excessive functions (i.e. the positive superharmonic functionsfromtheclassical… Meer...

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Potential Theory and Right Processes
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Potential Theory and Right Processes - nieuw boek

ISBN: 9789048166718

The developmentsin the recent yearsof the potential theoryemphasized a classof functions larger than that of excessive functions (i.e. the positive superharmonic functionsfromtheclassical… Meer...

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Potential Theory and Right Processes - pocketboek

ISBN: 9789048166718

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Boboc, Nicu; Beznea, Lucian:
Potential Theory and Right Processes - pocketboek

2010, ISBN: 9048166713

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Potential Theory and Right Processes by Lucian Beznea Paperback | Indigo Chapters

This book develops the potential theory starting from a sub-Markovian resolvent of kernels on a measurable space, covering the context offered by a right process with general state space. It turns out that the main results from the classical cases (e.g., on locally compact spaces, with Green functions) have meaningful extensions to this setting. The study of the strongly supermedian functions and specific methods like the Revuz correspondence, for the largest class of measures, and the weak duality between two sub-Markovian resolvents of kernels are presented for the first time in a complete form. It is shown that the quasi-regular semi-Dirichlet forms fit in the weak duality hypothesis. Further results are related to the subordination operators and measure perturbations. The subject matter is supplied with a probabilistic counterpart, involving the homogeneous random measures, multiplicative, left and co-natural additive functionals. The book is almost self-contained, being accessible to graduate students.

Gedetalleerde informatie over het boek. - Potential Theory and Right Processes by Lucian Beznea Paperback | Indigo Chapters


EAN (ISBN-13): 9789048166718
ISBN (ISBN-10): 9048166713
Gebonden uitgave
pocket book
Verschijningsjaar: 2010
Uitgever: Lucian Beznea
380 Bladzijden
Gewicht: 0,574 kg
Taal: eng/Englisch

Boek bevindt zich in het datenbestand sinds 2011-07-22T14:28:36+02:00 (Amsterdam)
Detailpagina laatst gewijzigd op 2023-04-11T21:55:54+02:00 (Amsterdam)
ISBN/EAN: 9789048166718

ISBN - alternatieve schrijfwijzen:
90-481-6671-3, 978-90-481-6671-8
alternatieve schrijfwijzen en verwante zoekwoorden:
Auteur van het boek: lucian, mertens mertens, meyer


Gegevens van de uitgever

Auteur: Lucian Beznea
Titel: Mathematics and Its Applications; Potential Theory and Right Processes
Uitgeverij: Springer; Springer Netherland
370 Bladzijden
Verschijningsjaar: 2010-12-07
Dordrecht; NL
Gedrukt / Gemaakt in
Taal: Engels
54,99 € (DE)

BC; Hardcover, Softcover / Mathematik/Analysis; Mathematische Analysis, allgemein; Verstehen; Dirichlet form; Median; Potential theory; brandonwiskunde; measure theory; random measure; Potential Theory; Probability Theory; Applications of Mathematics; Mathematical and Computational Biology; Wahrscheinlichkeitsrechnung und Statistik; Stochastik; Angewandte Mathematik; DV-gestützte Biologie/Bioinformatik; BB; EA

1 Excessive Functions.- 1.1 Sub-Markovian resolvent of kernels.- 1.2 Basics on excessive functions.- 1.3 Fine topology.- 1.4 Excessive measures.- 1.5 Ray topology and compactification.- 1.6 The reduction operation and the associated capacities.- 1.7 Polar and semipolar sets. Nearly measurable functions.- 1.8 Probabilistic interpretations: Sub-Markovian resolvents and right processes.- 2 Cones of Potentials and H-Cones.- 2.1 Basics on cones of potentials and H-cones.- 2.2 ?-Balayages on cones of potentials.- 2.3 Balayages on H-cones.- 2.4 Quasi bounded, subtractive and regular elements of a cone of potentials.- 3 Fine Potential Theoretical Techniques.- 3.1 Cones of potentials associated with a sub-Markovian resolvent.- 3.2 Regular excessive functions, fine carrier and semipolarity.- 3.3 Representation of balayages on excessive measures.- 3.4 Quasi bounded, regular and subtractive excessive measures.- 3.5 Tightness for sub-Markovian resolvents.- 3.6 Localization in excessive functions and excessive measures.- 3.7 Probabilistic interpretations: Continuous additive functionals and standardness.- 4 Strongly Supermedian Functions and Kernels.- 4.1 Supermedian functionals.- 4.2 Supermedian ?-quasi kernels.- 4.3 Strongly supermedian functions.- 4.4 Fine densities.- 4.5 Probabilistic interpretations: Homogeneous random measures.- 5 Subordinate Resolvents.- 5.1 Weak subordination operators.- 5.2 Inverse subordination.- 5.3 Probabilistic interpretations: Multiplicative functionals.- 6 Revuz Correspondence.- 6.1 Revuz measures.- 6.2 Hypothesis (B) of Hunt.- 6.3 Smooth measures and sub-Markovian resolvents.- 6.4 Measure perturbation of sub-Markovian resolvents.- 6.5 Probabilistic interpretations: Positive left additive functionals.- 7 Resolvents under Weak Duality Hypothesis.- 7.1Weak duality hypothesis.- 7.2 Natural potential kernels and the Revuz correspondence.- 7.3 Smooth and cosmooth measures.- 7.4 Subordinate resolvents in weak duality.- 7.5 Semi-Dirichlet forms.- 7.6 Weak duality induced by a semi-Dirichlet form.- 7.7 Probabilistic interpretations: Multiplicative functionals in weak duality.- A Appendix.- A.1 Complements on measure theory, kernels, Choquet boundary and capacity.- A.2 Complements on right processes.- A.4 Basics on coercive closed bilinear forms.- Notes.

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9781402024979 Potential Theory and Right Processes (50-99.99)


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