Abstract
It is known that if the Lévy measure of a Lévy process X(t), 0≤t≤1, is "heavy tailed", then the right tails of sup0≤t≤1X(t) and X(1) are of the same rate of decay. One of the results of this note is a description of a class of compound Poisson processes with negative drift and "light" tails (which is a subclass of Lévy processes) such that these tails are incomparable.
Original language | English |
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Pages (from-to) | 145-156 |
Number of pages | 12 |
Journal | Stochastic Processes and their Applications |
Volume | 90 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jan 2000 |
Keywords
- Compound poisson process
- Lévy process
- Tail behavior
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics