École d'Été de Probabilités de Saint-Flour

Brownian Motion and its Applications to Mathematical Analysis

École d'Été de Probabilités de Saint-Flour XLIII – 2013

Authors: Burdzy, Krzysztof

  • Contains interesting examples of couplings
  • Gentle introduction to Brownian motion and analysis
  • Heuristic explanations of the main results
see more benefits

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-04394-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-319-04393-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this book

These lecture notes provide an introduction to the applications of Brownian motion to analysis and more generally, connections between Brownian motion and analysis. Brownian motion is a well-suited model for a wide range of real random phenomena, from chaotic oscillations of microscopic objects, such as flower pollen in water, to stock market fluctuations. It is also a purely abstract mathematical tool which can be used to prove theorems in "deterministic" fields of mathematics.

The notes include a brief review of Brownian motion and a section on probabilistic proofs of classical theorems in analysis. The bulk of the notes are devoted to recent (post-1990) applications of stochastic analysis to Neumann eigenfunctions, Neumann heat kernel and the heat equation in time-dependent domains.

Table of contents (10 chapters)

  • Brownian Motion

    Burdzy, Krzysztof

    Pages 1-10

  • Probabilistic Proofs of Classical Theorems

    Burdzy, Krzysztof

    Pages 11-19

  • Overview of the “Hot Spots” Problem

    Burdzy, Krzysztof

    Pages 21-29

  • Neumann Eigenfunctions and Eigenvalues

    Burdzy, Krzysztof

    Pages 31-39

  • Synchronous and Mirror Couplings

    Burdzy, Krzysztof

    Pages 41-62

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-04394-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-319-04393-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Brownian Motion and its Applications to Mathematical Analysis
Book Subtitle
École d'Été de Probabilités de Saint-Flour XLIII – 2013
Authors
Series Title
École d'Été de Probabilités de Saint-Flour
Series Volume
2106
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-04394-4
DOI
10.1007/978-3-319-04394-4
Softcover ISBN
978-3-319-04393-7
Series ISSN
0721-5363
Edition Number
1
Number of Pages
XII, 137
Number of Illustrations and Tables
12 b/w illustrations, 4 illustrations in colour
Topics