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Selfdecomposability perpetuity laws and stopping times

Jurek Z. J.

Probability and Mathematical Statistics

1999

Vol. 19, Fasc. 2

413--419

The decomposability property of Lévy class L of probability distributions, on a Banach space, is extended to a family of stopping times associated with background driving Lévy processes (BDLP). As consequences, this allows us to show that all selfdecomposable measures are perpetuity laws and to get a representation of gamma distribution as an infinite product of independent uniform distributions.