Classical Potential Theory and Its Probabilistic Counterpart

Name: Classical Potential Theory and Its Probabilistic Counterpart
Brand: Springer, Berlin
SKU: 9781461297383
Price: 462.05 RON
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Advanced Problems

Autor: J. L. Doob

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Editura: Springer, Berlin

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Potential theory and certain aspects of probability theory are intimately related, perhaps most obvi...

Informații despre carte

Autor

J. L. Doob

Limbă

engleză

Legare

Carte - Carte broșată

Publicat

2011

Pagini

847

EAN

9781461297383

Enbook ID

02180168

Editura

Springer, Berlin

Greutate

1318

Dimensiuni

155 x 235

Descriere completă

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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Classical Potential Theory and Its Probabilistic Counterpart

Advanced Problems

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Descriere completă

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