## Annals of Applied Probability

### Cramér’s estimate for a reflected Lévy process

#### Abstract

The natural analogue for a Lévy process of Cramér’s estimate for a reflected random walk is a statement about the exponential rate of decay of the tail of the characteristic measure of the height of an excursion above the minimum. We establish this estimate for any Lévy process with finite negative mean which satisfies Cramér’s condition, and give an explicit formula for the limiting constant. Just as in the random walk case, this leads to a Poisson limit theorem for the number of “high excursions.”

#### Article information

Source
Ann. Appl. Probab., Volume 15, Number 2 (2005), 1445-1450.

Dates
First available in Project Euclid: 3 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1115137981

Digital Object Identifier
doi:10.1214/105051605000000016

Mathematical Reviews number (MathSciNet)
MR2134110

Zentralblatt MATH identifier
1272.68116

#### Citation

Doney, R. A.; Maller, R. A. Cramér’s estimate for a reflected Lévy process. Ann. Appl. Probab. 15 (2005), no. 2, 1445--1450. doi:10.1214/105051605000000016. https://projecteuclid.org/euclid.aoap/1115137981

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