The Annals of Probability

Distributions of Subadditive Functionals of Sample Paths of Infinitely Divisible Processes

Jan Rosinski and Gennady Samorodnitsky

Full-text: Open access

Abstract

Subadditive functionals on the space of sample paths include suprema, integrals of paths, oscillation on sets and many others. In this paper we find an optimal condition which ensures that the distribution of a subadditive functional of sample paths of an infinitely divisible process belongs to the subexponential class of distributions. Further, we give exact tail behavior for the distributions of such functionals, thus improving many recent results obtained for particular forms of subadditive functionals and for particular infinitely divisible processes.

Article information

Source
Ann. Probab., Volume 21, Number 2 (1993), 996-1014.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989279

Digital Object Identifier
doi:10.1214/aop/1176989279

Mathematical Reviews number (MathSciNet)
MR1217577

Zentralblatt MATH identifier
0776.60049

JSTOR
links.jstor.org

Subjects
Primary: 60G07: General theory of processes
Secondary: 60E07: Infinitely divisible distributions; stable distributions 60G57: Random measures 60H05: Stochastic integrals

Keywords
Subexponential distributions infiniely divisible processes tail behavior of the distributions of functionals of sample paths stable processes

Citation

Rosinski, Jan; Samorodnitsky, Gennady. Distributions of Subadditive Functionals of Sample Paths of Infinitely Divisible Processes. Ann. Probab. 21 (1993), no. 2, 996--1014. doi:10.1214/aop/1176989279. https://projecteuclid.org/euclid.aop/1176989279


Export citation