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

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Selected Works of Donald L. Burkholder

Part of the book series: Selected Works in Probability and Statistics ((SWPS))

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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:

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

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Author information

Authors and Affiliations

  1. Department of Mathematics and Department of Statistics, Purdue University, West Lafayette, IN, 47907-2068, USA

    Burgess Davis

  2. Department of Mathematics, University of Illinois, Urbana, IL, 61801, USA

    Renming Song

Authors
  1. Burgess Davis
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  2. Renming Song
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Correspondence to Burgess Davis .

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Editors and Affiliations

  1. , Department of Mathematics and, Purdue University, N. University Street 150, West Lafayette, 47907-2068, Indiana, USA

    Burgess Davis

  2. , Department of Mathematics, University of Illinois, Urbana, W. Green St. 1409, Urbana, 61801, Illinois, USA

    Renming Song

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Davis, B., Song, R. (2011). Exit Times of Brownian Motion, Harmonic Majorization, and Hardy Spaces. In: Davis, B., Song, R. (eds) Selected Works of Donald L. Burkholder. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7245-3_18

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