Verwandte Artikel zu Classical Potential Theory and Its Probabilistic Counterpart...
Classical Potential Theory and Its Probabilistic Counterpart (Grundlehren Der Mathematischen Wissenschaften) - Hardcover
Inhaltsangabe
Potential theory and certain aspects of probability theory are intimately related, perhaps most obviously in that the transition function determining a Markov process can be used to define the Green function of a potential theory. Thus it is possible to define and develop many potential theoretic concepts probabilistically, a procedure potential theorists observe withjaun diced eyes in view of the fact that now as in the past their subject provides the motivation for much of Markov process theory. However that may be it is clear that certain concepts in potential theory correspond closely to concepts in probability theory, specifically to concepts in martingale theory. For example, superharmonic functions correspond to supermartingales. More specifically: the Fatou type boundary limit theorems in potential theory correspond to supermartingale convergence theorems; the limit properties of monotone sequences of superharmonic functions correspond surprisingly closely to limit properties of monotone sequences of super martingales; certain positive superharmonic functions [supermartingales] are called "potentials," have associated measures in their respective theories and are subject to domination principles (inequalities) involving the supports of those measures; in each theory there is a reduction operation whose properties are the same in the two theories and these reductions induce sweeping (balayage) of the measures associated with potentials, and so on.
Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.
Reseña del editor
Potential theory and certain aspects of probability theory are intimately related, perhaps most obviously in that the transition function determining a Markov process can be used to define the Green function of a potential theory. Thus it is possible to define and develop many potential theoretic concepts probabilistically, a procedure potential theorists observe withjaun diced eyes in view of the fact that now as in the past their subject provides the motivation for much of Markov process theory. However that may be it is clear that certain concepts in potential theory correspond closely to concepts in probability theory, specifically to concepts in martingale theory. For example, superharmonic functions correspond to supermartingales. More specifically: the Fatou type boundary limit theorems in potential theory correspond to supermartingale convergence theorems; the limit properties of monotone sequences of superharmonic functions correspond surprisingly closely to limit properties of monotone sequences of super martingales; certain positive superharmonic functions [supermartingales] are called "potentials," have associated measures in their respective theories and are subject to domination principles (inequalities) involving the supports of those measures; in each theory there is a reduction operation whose properties are the same in the two theories and these reductions induce sweeping (balayage) of the measures associated with potentials, and so on.
„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.
Neu kaufen
Diesen Artikel anzeigen
EUR 36,01
EUR 29,87 für den Versand von USA nach Deutschland
Versandziele, Kosten & DauerWeitere beliebte Ausgaben desselben Titels
Suchergebnisse für Classical Potential Theory and Its Probabilistic Counterpart...
Internationale Ausgabe
Classical Potential Theory and Its Probabilistic Counterpart
Verlag:
Secaucus, New Jersey, U.S.A.: Springer Verlag, 1984
ISBN 10: 0387908811
ISBN 13: 9780387908816
Neu
Soft cover
Anbieter: Sizzler Texts, SAN GABRIEL, CA, USA
Verkäuferbewertung 5 von 5 Sternen
Soft cover. Zustand: New. Zustand des Schutzumschlags: New. 1st Edition. **INTERNATIONAL EDITION** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments go through via USPS/UPS/DHL with tracking numbers. Great professional textbook selling experience and expedite shipping service. Bestandsnummer des Verkäufers ABE-10833602265
Anzahl: 5 verfügbar
Internationale Ausgabe
Classical Potential Theory and Its Probabilistic Counterpart
Internationale AusgabeAnbieter: Aideo Books, San Marino, CA, USA
Verkäuferbewertung 5 von 5 Sternen
Trade paperback. Zustand: New in new dust jacket. First edition. ***INTERNATIONAL EDITION*** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments contain tracking numbers. Great professional textbook selling experience and expedite shipping service. Glued binding. Cloth over boards. 846 p. Contains: Illustrations. Grundlehren Der Mathematischen Wissenschaften (Springer Hardcover), 262. Audience: General/trade. Bestandsnummer des Verkäufers K4470000522
Anzahl: 20 verfügbar