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Classical potential theory and its probabilistic counterpart

Classical potential theory and its probabilistic counterpart Acta Applicandae Mathematicae 6 (1986) 213 Book Reviews J. L. Doob: Classical Potential Theory and its Probabilistic Counterpart, Springer- Verlag, Berlin, Heidelberg, New York, 1984. This book has previously been reviewed by P. A. Meyer in Bull. A.M.S. 12 (1985) 177-181 and includes, in addition, much about potential theory which I can hardly hope to add to. As P. A. Meyer says, "this is a great work, large in its dimensions and in the amount of material covered". The job of reviewing for Acta Applicandae Mathematicae was undertaken with quite a bit of hesitation and I freely admit that the review below does not really do justice. And with this warning, we may proceed. The book is divided into three parts. The first part is purely analytic, the second part probabilistic, and the third part a mixture. I was able to look at the first part in some detail, the second in much less detail, but did not have the energy for the third. Part 1: Chapters 1 through 4 cover such basic material as harmonic and superhamonic functions, Harnack's theorems, the Dirichlet problem etc. There are some extras such as boundary limits for quotients (Doob's own work); an http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Classical potential theory and its probabilistic counterpart

Acta Applicandae Mathematicae , Volume 6 (2) – May 1, 2004
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Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF00046726
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Abstract

Acta Applicandae Mathematicae 6 (1986) 213 Book Reviews J. L. Doob: Classical Potential Theory and its Probabilistic Counterpart, Springer- Verlag, Berlin, Heidelberg, New York, 1984. This book has previously been reviewed by P. A. Meyer in Bull. A.M.S. 12 (1985) 177-181 and includes, in addition, much about potential theory which I can hardly hope to add to. As P. A. Meyer says, "this is a great work, large in its dimensions and in the amount of material covered". The job of reviewing for Acta Applicandae Mathematicae was undertaken with quite a bit of hesitation and I freely admit that the review below does not really do justice. And with this warning, we may proceed. The book is divided into three parts. The first part is purely analytic, the second part probabilistic, and the third part a mixture. I was able to look at the first part in some detail, the second in much less detail, but did not have the energy for the third. Part 1: Chapters 1 through 4 cover such basic material as harmonic and superhamonic functions, Harnack's theorems, the Dirichlet problem etc. There are some extras such as boundary limits for quotients (Doob's own work); an

Journal

Acta Applicandae Mathematicae – Springer Journals

Published: May 1, 2004

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