The Annals of Probability
- Ann. Probab.
- Volume 9, Number 2 (1981), 330-334.
Comparison Theorems for Sample Function Growth
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.
Ann. Probab., Volume 9, Number 2 (1981), 330-334.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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