The Annals of Probability

Comparison Theorems for Sample Function Growth

P. W. Millar

Full-text: Open access

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.

Article information

Source
Ann. Probab., Volume 9, Number 2 (1981), 330-334.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994476

Digital Object Identifier
doi:10.1214/aop/1176994476

Mathematical Reviews number (MathSciNet)
MR606997

Zentralblatt MATH identifier
0471.60045

JSTOR
links.jstor.org

Subjects
Primary: 60G17: Sample path properties
Secondary: 60J30 60J25: Continuous-time Markov processes on general state spaces 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Keywords
Stationary independent increments Markov process sample functions minimum last exit time local time

Citation

Millar, P. W. Comparison Theorems for Sample Function Growth. Ann. Probab. 9 (1981), no. 2, 330--334. doi:10.1214/aop/1176994476. https://projecteuclid.org/euclid.aop/1176994476


Export citation