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 ...
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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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Add this copy of Classical Potential Theory and Its Probabilistic to cart. $44.97, very good condition, Sold by ThriftBooks-Dallas rated 5.0 out of 5 stars, ships from Dallas, TX, UNITED STATES, published 2001 by Springer.
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Very Good. Size: 6x1x9; Springer Verlag; Berlin, 2001. Trade paperback. Reprint of the 1984 Edition. A Very Good, binding sturdy and intact, some handling/scuff marks to covers, bit of cover edge/corner wear, few scuff and smudge marks to text block edges, soiled spot top title page and top frontispiece crease top corner page 223/224, a nice, overall clean and unmarked copy in wraps. 8vo[octavo or approx. 6 x 9], 846pp., bibliography, indexed. We pack securely and ship daily w/delivery confirmation on every book. The picture on the listing page is of the actual book for sale. Additional Scan(s) are available for any item, please inquire.
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