The Annals of Probability

The Behavior of Asymmetric Cauchy Processes for Large Time

William E. Pruitt and S. James Taylor

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Abstract

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.

Article information

Source
Ann. Probab., Volume 11, Number 2 (1983), 302-327.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993598

Digital Object Identifier
doi:10.1214/aop/1176993598

Mathematical Reviews number (MathSciNet)
MR690130

Zentralblatt MATH identifier
0514.60046

JSTOR
links.jstor.org

Subjects
Primary: 60G17: Sample path properties
Secondary: 60J30

Keywords
Potential theory hitting probabilities rate of escape holes in range Lebesgue measure of range

Citation

Pruitt, William E.; Taylor, S. James. The Behavior of Asymmetric Cauchy Processes for Large Time. Ann. Probab. 11 (1983), no. 2, 302--327. doi:10.1214/aop/1176993598. https://projecteuclid.org/euclid.aop/1176993598


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