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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.
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Edizione Internazionale
Classical Potential Theory and Its Probabilistic Counterpart
Editore:
Secaucus, New Jersey, U.S.A.: Springer Verlag, 1984
ISBN 10: 0387908811
ISBN 13: 9780387908816
Nuovo
Soft cover
Da: Sizzler Texts, SAN GABRIEL, CA, U.S.A.
Valutazione del venditore 5 su 5 stelle
Soft cover. Condizione: New. Condizione sovraccoperta: 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. Codice articolo ABE-10833602265
Quantità: 5 disponibili
Edizione Internazionale
Classical Potential Theory and Its Probabilistic Counterpart
Editore:
Springer, New York, NY, 1984
ISBN 10: 0387908811
ISBN 13: 9780387908816
Nuovo
Trade paperback
Da: Aideo Books, San Marino, CA, U.S.A.
Valutazione del venditore 5 su 5 stelle
Trade paperback. Condizione: 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. Codice articolo K4470000522
Quantità: 20 disponibili