No Words Wasted Sale
 
 

Special Offers see all

Enter to WIN a $100 Credit

Subscribe to PowellsBooks.news
for a chance to win.
Privacy Policy

Visit our stores


    Recently Viewed clear list


    Required Reading | January 16, 2015

    Required Reading: Books That Changed Us



    We tend to think of reading as a cerebral endeavor, but every once in a while, it can spur action. The following books — ranging from... Continue »

    spacer
Qualifying orders ship free.
$77.50
New Trade Paper
Ships in 1 to 3 days
Add to Wishlist
available for shipping or prepaid pickup only
Available for In-store Pickup
in 7 to 12 days
Qty Store Section
25 Remote Warehouse Mathematics- Functional Analysis

This title in other editions

Classical Potential Theory and Its Probabilistic Counterpart (Classics in Mathematics)

by

Classical Potential Theory and Its Probabilistic Counterpart (Classics in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

From the reviews: "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)

Synopsis:

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)

Description:

Includes bibliographical references (p. [819]-825) and indexes.

About the Author

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)

Table of 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.

Product Details

ISBN:
9783540412069
Author:
Doob, Joseph L.
Author:
Doob, J. I.
Publisher:
Springer
Location:
Berlin, Heidelberg
Subject:
Probability
Subject:
Functional Analysis
Subject:
Martingales (mathematics)
Subject:
Harmonic functions
Subject:
Potential theory (mathematics)
Subject:
Martingales.
Subject:
Potential theory
Subject:
Probability & Statistics - General
Subject:
Mathematical Analysis
Subject:
31XX
Subject:
60J45
Subject:
Probabilistic Potential Theory
Subject:
Probability Theory and Stochastic Processes
Subject:
Mathematics : Functional Analysis
Subject:
Vector Analysis
Subject:
Mathematics
Subject:
The Arts
Subject:
mathematics and statistics
Subject:
Distribution (Probability theory)
Copyright:
Edition Description:
1st ed. 1984. Reprint
Series:
Classics in Mathematics
Series Volume:
EDO-HE-1999-9
Publication Date:
20010301
Binding:
TRADE PAPER
Language:
English
Pages:
1601
Dimensions:
235 x 155 mm 1280 gr

Other books you might like

  1. Operator Theory, Advances and... New Hardcover $200.95
  2. Brownian Motion & Stochastic Calculu... New Trade Paper $72.50
  3. The Geometry of Schemes (Universitext) New Trade Paper $56.95

Related Subjects

Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

Classical Potential Theory and Its Probabilistic Counterpart (Classics in Mathematics) New Trade Paper
0 stars - 0 reviews
$77.50 In Stock
Product details 1601 pages Springer-Verlag - English 9783540412069 Reviews:
"Synopsis" by , 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)

spacer
spacer
  • back to top

FOLLOW US ON...

     
Powell's City of Books is an independent bookstore in Portland, Oregon, that fills a whole city block with more than a million new, used, and out of print books. Shop those shelves — plus literally millions more books, DVDs, and gifts — here at Powells.com.