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Weak Inequalities for Exit Times and Analytic Functions

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

Abstract

We give a method for obtaining inequalities of the form
$$ \mathop {\sup}\limits_{\lambda >0} \Phi \left( \lambda \right)P\left( {f >\lambda } \right) \leq \,c \mathop {\sup}\limits_{\lambda >0} \Phi \,(\lambda)P\left( {g >\lambda } \right)$$
(1)
and then use it to obtain some results about exit times of Brownian motion and analytic functions supplementing those of [3].

Keywords

Brownian Motion Maximal Function Harmonic Measure Exit Time Positive Zero 
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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