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Brownian motion

Author: Peter Mörters; Y Peres; Oded Schramm; Wendelin Werner
Publisher: Cambridge, UK ; New York : Cambridge University Press, ©2010.
Series: Cambridge series on statistical and probabilistic mathematics, 30.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
"This textbook offers a broad and deep exposition of Brownian motion. Extensively class tested, it leads the reader from the basics to the latest research in the area." "Starting with the construction of Brownian motion, the book then proceeds to sample path properties such as continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine  Read more...
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Document Type: Book
All Authors / Contributors: Peter Mörters; Y Peres; Oded Schramm; Wendelin Werner
ISBN: 9780521760188 0521760186
OCLC Number: 466341039
Description: xii, 403 pages : illustrations ; 26 cm.
Contents: Preface; Frequently used notation; Motivation; 1. Brownian motion as a random function; 2. Brownian motion as a strong Markov process; 3. Harmonic functions, transience and recurrence; 4. Hausdorff dimension: techniques and applications; 5. Brownian motion and random walk; 6. Brownian local time; 7. Stochastic integrals and applications; 8. Potential theory of Brownian motion; 9. Intersections and self-intersections of Brownian paths; 10. Exceptional sets for Brownian motion; Appendix A. Further developments: 11. Stochastic Loewner evolution and its applications to planar Brownian motion; Appendix B. Background and prerequisites; Hints and solutions for selected exercises; References; Index.
Series Title: Cambridge series on statistical and probabilistic mathematics, 30.
Responsibility: Peter Mörters and Yuval Peres ; with an appendix by Oded Schramm and Wendelin Werner.

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Everything the graduate student in probability wants to know about Brownian motion, including the latest research in the field.  Read more...

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'This splendid account of the modern theory of Brownian motion puts special emphasis on sample path properties and connections with harmonic functions and potential theory, without omitting such Read more...

 
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schema:reviewBody""This textbook offers a broad and deep exposition of Brownian motion. Extensively class tested, it leads the reader from the basics to the latest research in the area." "Starting with the construction of Brownian motion, the book then proceeds to sample path properties such as continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool, and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes."--Jacket."
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