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

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


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:
$$\tau \left( \omega \right) = \inf \left\{ {t >0:{X_t}(\omega) \notin R} \right\}.$$


Brownian Motion Hardy Space Optimal Choice Harmonic Measure Exit Time 
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© 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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