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Exit Times of Brownian Motion, Harmonic Majorization, and Hardy Spaces

  • Burgess Davis
  • Renming Song
Chapter
Part of the Selected Works in Probability and Statistics book series (SWPS)

Abstract

Let R be an open, connected subset of R n \(n \geqslant 2\), X a Brownian motion in R n starting at a point x in R, and \(\tau\) the first time X leaves R:
$$\tau \left( \omega \right) = \inf \left\{ {t >0:{X_t}(\omega) \notin R} \right\}.$$

Keywords

Brownian Motion Hardy Space Optimal Choice Harmonic Measure Exit Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematics and Department of StatisticsPurdue UniversityWest LafayetteUSA
  2. 2.Department of MathematicsUniversity of IllinoisUrbanaUSA

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