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May, 1983 The Behavior of Asymmetric Cauchy Processes for Large Time
William E. Pruitt, S. James Taylor
Ann. Probab. 11(2): 302-327 (May, 1983). DOI: 10.1214/aop/1176993598


This paper develops precise estimates for the potential kernel, capacities of large intervals, and the probabilities of hitting large intervals for the asymmetric Cauchy processes. These are then applied to study three problems concerning the sample paths: (i) the rate of escape of $|X_t|$ as $t \rightarrow \infty$; (ii) the sizes of the large holes in the range of the process; (iii) the asymptotic behavior of the Lebesgue measure of that part of the range of the process that is in a large interval.


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William E. Pruitt. S. James Taylor. "The Behavior of Asymmetric Cauchy Processes for Large Time." Ann. Probab. 11 (2) 302 - 327, May, 1983.


Published: May, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0514.60046
MathSciNet: MR690130
Digital Object Identifier: 10.1214/aop/1176993598

Primary: 60G17
Secondary: 60J30

Keywords: hitting probabilities , holes in range , Lebesgue measure of range , potential theory , Rate of escape

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 2 • May, 1983
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