Positive harmonic functions and diffusion: an integrated analytic and probabilistic approach / Ross G. Pinsky

Auteur: Pinsky, Ross G. (1955-) - AuteurType de document: MonographieCollection: Cambridge studies in advanced mathematics ; 45Langue: anglaisPays: Grande BretagneÉditeur: Cambridge : Cambridge University Press, 1995Description: 1 vol. (XVI- 474 p.) ; 24 cm ISBN: 0521470145 ; rel. Résumé: The author gives a thorough account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach. Many results that form the folklore of the subject or are published by the author and many others somewhere during the last decades are given here a rigorous and largely self-contained exposition. At quite a number of places, the author presents his own proof, and some of the results are entirely new. ... Each chapter is complemented by many exercises. In some of them the reader is asked to supply a proof or a step of a proof omitted from the text. For that reason, generous hints are given. Each chapter ends with historical notes giving many references. Apparently, the book is written with great care, and it is a pleasure to read it. (Zentralblatt).Bibliographie: Bibliogr. p. [461] à 470. Index. Sujets MSC: 31C05 Potential theory -- Other generalizations -- Harmonic, subharmonic, superharmonic functions
31C35 Potential theory -- Other generalizations -- Martin boundary theory
60G44 Probability theory and stochastic processes -- Stochastic processes -- Martingales with continuous parameter
60H05 Probability theory and stochastic processes -- Stochastic analysis -- Stochastic integrals
60J60 Probability theory and stochastic processes -- Markov processes -- Diffusion processes
En-ligne: Zentralblatt | MathSciNet
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Bibliogr. p. [461] à 470. Index

The author gives a thorough account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach. Many results that form the folklore of the subject or are published by the author and many others somewhere during the last decades are given here a rigorous and largely self-contained exposition. At quite a number of places, the author presents his own proof, and some of the results are entirely new. ... Each chapter is complemented by many exercises. In some of them the reader is asked to supply a proof or a step of a proof omitted from the text. For that reason, generous hints are given. Each chapter ends with historical notes giving many references.

Apparently, the book is written with great care, and it is a pleasure to read it. (Zentralblatt)

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