Brownian Motion and its Applications to Mathematical Analysis

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

  • Krzysztof Burdzy

Part of the Lecture Notes in Mathematics book series (LNM, volume 2106)

Also part of the École d'Été de Probabilités de Saint-Flour book sub series (LNMECOLE, volume 2106)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Krzysztof Burdzy
    Pages 1-10
  3. Krzysztof Burdzy
    Pages 11-19
  4. Krzysztof Burdzy
    Pages 21-29
  5. Krzysztof Burdzy
    Pages 31-39
  6. Krzysztof Burdzy
    Pages 41-62
  7. Krzysztof Burdzy
    Pages 63-75
  8. Krzysztof Burdzy
    Pages 77-87
  9. Krzysztof Burdzy
    Pages 89-96
  10. Krzysztof Burdzy
    Pages 97-105
  11. Back Matter
    Pages 133-140

About this book

Introduction

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.

Keywords

"hot spots" conjecture 60J65, 60H30, 60G17 Brownian motion Neumann eigenfunction coupling heat equation

Authors and affiliations

  • Krzysztof Burdzy
    • 1
  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-04394-4
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-04393-7
  • Online ISBN 978-3-319-04394-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
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