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April, 1981 Comparison Theorems for Sample Function Growth
P. W. Millar
Ann. Probab. 9(2): 330-334 (April, 1981). DOI: 10.1214/aop/1176994476

Abstract

The growth rate at 0 of a Levy process is compared with the growth rate at a local minimum, $m$, of the process. For the lim inf it is found that the growth rate at $m$ is the same as that on the set of "ladder points" following 0, parameterized by inverse local time; this result gives a precise meaning to the notion that a Levy process leaves its minima "faster" than it leaves 0. A less precise result is obtained for the lim sup.

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P. W. Millar. "Comparison Theorems for Sample Function Growth." Ann. Probab. 9 (2) 330 - 334, April, 1981. https://doi.org/10.1214/aop/1176994476

Information

Published: April, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0471.60045
MathSciNet: MR606997
Digital Object Identifier: 10.1214/aop/1176994476

Subjects:
Primary: 60G17
Secondary: 60G40 , 60J25 , 60J30

Keywords: last exit time , Local time , Markov process , minimum , sample functions , stationary independent increments

Rights: Copyright © 1981 Institute of Mathematical Statistics

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Vol.9 • No. 2 • April, 1981
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