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Author Doob, Joseph L.

Title Classical Potential Theory and Its Probabilistic Counterpart [electronic resource] / by Joseph L. Doob.

Published Berlin, Heidelberg : Springer Berlin Heidelberg, 2001.


Location Call No. Status
Physical description 1 online resource (l, 1551 pages).
Series Classics in Mathematics, 1431-0821
Classics in mathematics.
Contents From the contents: Introduction -- Notation and Conventions -- Part I Classical and Parabolic Potential Theory: Introduction to the Mathematical Background of Classical Potential Theory; Basic Properties of Harmonic, Subharmonic, and Superharmonic Functions; Infirma of Families of Suerharmonic Functions; Potentials on Special Open sets; Polar sets and Their Applications; The Fundamental Convergence Theorem and the Reduction Operation; Green Functions; The Dirichlet Problem for Relative Harmonic Functions; Lattices and Related Classes of Functions; The Sweeping Operation, The Fine Topology; The Martin Boundary; Classical Energy and Capacity; One-Dimensional Potential Theory -- ... Part II Probabilistic Counterpart of Part I ... -- Part III Lattices in Classical Potential Theory and Martingale Theory; Brownian Motion and the PWB Method; Brownian Motion on the Martin Space -- Appendixes.
Summary From the reviews: "This huge book written in several years by one of the few mathematicians able to do it, appears as a precise and impressive study (not very easy to read) of this bothsided question that replaces, in a coherent way, without being encyclopaedic, a large library of books and papers scattered without a uniform language. Instead of summarizing the author gives his own way of exposition with original complements. This requires no preliminary knowledge. ... The purpose which the author explains in his introduction, i.e. a deep probabilistic interpretation of potential theory and a link between two great theories, appears fulfilled in a masterly manner". M. Brelot in Metrika (1986).
Subject Mathematics.
Potential theory (Mathematics)
Distribution (Probability theory)
Electronic books.
ISBN 9783642565731 (electronic bk.)
3642565735 (electronic bk.)