Convolution equivalence and infinite divisibility

Convolution equivalence and infinite divisibility

Known results relating the tail behaviour of a compound Poisson distribution function to that of its Lévy measure when one of them is convolution equivalent are extended to general infinitely divisible distributions. A tail equivalence result is obtained for random sum distributions in which the sum...

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Veröffentlicht in:Journal of applied probability 2004-06, Vol.41 (2), p.407-424
1. Verfasser: Pakes, Anthony G.
Format: Artikel
Sprache:eng
Schlagworte:
60E07
60F99
Clines
convolution equivalence
Density
Distribution functions
Distribution theory
Division
Equivalence relation
Exact sciences and technology
infinite divisibility
Infinity
Mathematical models
Mathematical theorems
Mathematics
Poisson distribution
Probability
Probability and statistics
Probability theory and stochastic processes
random sum
Random variables
Real lines
Research Papers
Sciences and techniques of general use
Studies
Subexponential distribution
tail equivalence
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Beschreibung
Zusammenfassung:Known results relating the tail behaviour of a compound Poisson distribution function to that of its Lévy measure when one of them is convolution equivalent are extended to general infinitely divisible distributions. A tail equivalence result is obtained for random sum distributions in which the summands have a two-sided distribution.
ISSN:0021-9002
1475-6072
DOI:10.1239/jap/1082999075