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October, 1988 Measuring Close Approaches on a Brownian Path
Edwin A. Perkins, S. James Taylor
Ann. Probab. 16(4): 1458-1480 (October, 1988). DOI: 10.1214/aop/1176991578


Integral tests are found for the uniform escape rate of a $d$-dimensional Brownian path $(d \geq 4)$, i.e., for the lower growth rate of $\inf\{|X(t) - X(s)|: 0 \leq s, t \leq 1, |t - s| \geq h\}$ as $h \downarrow 0$. The gap between this uniform escape rate and the one-sided local escape rate of Dvoretsky and Erdos and the two-sided local escape rate of Jain and Taylor suggest the study of certain sets of times of slow one- or two-sided escape. The Hausdorff dimension of these exceptional sets is computed. The results are proved for a broad class of strictly stable processes.


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Edwin A. Perkins. S. James Taylor. "Measuring Close Approaches on a Brownian Path." Ann. Probab. 16 (4) 1458 - 1480, October, 1988.


Published: October, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0659.60113
MathSciNet: MR958197
Digital Object Identifier: 10.1214/aop/1176991578

Primary: 60J65
Secondary: 60G17 , 60J30

Keywords: Brownian motion , Hausdorff dimension , Integral test , Stable process , two-sided escape rate , uniform escape rate

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 4 • October, 1988
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