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Classics in Mathematics

Classical Potential Theory and Its Probabilistic Counterpart

Authors: Doob, Joseph L.

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About this book

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)

About the authors

Biography of Joseph L. Doob

Born in Cincinnati, Ohio on February 27, 1910, Joseph L. Doob studied for both his undergraduate and doctoral degrees at Harvard University. He was appointed to the University of Illinois in 1935 and remained there until his retirement in 1978.

Doob worked first in complex variables, then moved to probability under the initial impulse of H. Hotelling, and influenced by A.N Kolmogorov's famous monograph of 1933, as well as by Paul Lévy's work.

In his own book Stochastic Processes (1953), Doob established martingales as a particularly important type of stochastic process. Kakutani's treatment of the Dirichlet problem in 1944, combining complex variable theory and probability, sparked off Doob's interest in potential theory, which culminated in the present book.

(For more details see: http://www.dartmouth.edu/~chance/Doob/conversation.html)

Reviews

From the reviews:

"In the early 1920's, Norbert Wiener wrote significant papers on the Dirichlet problem and on Brownian motion. Since then there has been enormous activity in potential theory and stochastic processes, in which both subjects have reached a high degree of polish and their close relation has been discovered. Here is a momumental work by Doob, one of the masters, in which Part 1 develops the potential theory associated with Laplace's equation and the heat equation, and Part 2 develops those parts (martingales and Brownian motion) of stochastic process theory which are closely related to Part 1". G.E.H. Reuter in Short Book Reviews (1985)

"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 fullfilled in a masterly manner". Metrika (1986)

"It is good news that Doob’s monumental book is now available at a very reasonable price. The impressive volume (846 pages!) is still the only book concentrating on a thorough presentation of the potential theory of the Laplace operator … . The material in the chapters on conditional Brownian motion and Brownian motion on the Martin space cannot easily be found in that depth elsewhere. A long appendix on various topics (more than 50 pages) and many historical notes complete this great ‘encyclopedia’." (Wolfhard Hansen, Zentralblatt MATH, Vol. 990 (15), 2002)


Table of contents (32 chapters)

Table of contents (32 chapters)

Buy this book

eBook $54.99
price for USA in USD (gross)
  • ISBN 978-3-642-56573-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-3-540-41206-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Classical Potential Theory and Its Probabilistic Counterpart
Authors
Series Title
Classics in Mathematics
Copyright
2001
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-56573-1
DOI
10.1007/978-3-642-56573-1
Softcover ISBN
978-3-540-41206-9
Series ISSN
1431-0821
Edition Number
1
Number of Pages
L, 1551
Additional Information
Originally published as Vol. 262 in the series: Grundlehren der mathematischen Wissenschaften
Topics