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Contents of PMS, Vol. 24, Fasc. 1,
pages 181 - 190
 

SELFDECOMPOSABLE LAWS ASSOCIATED WITH HYPERBOLIC FUNCTIONS

Zbigniew J. Jurek
Marc Yor

Abstract: It is shown that the hyperbolic functions can be associated with selfdecomposable distributions (in short: SD probability distributions or Lévy class L of probability laws). Consequently, they admit associated background driving Lévy processes Y (BDLP’s Y). We interpret the distributions of Y (1) via Bessel squared processes, Bessel bridges and local times.

2000 AMS Mathematics Subject Classification: Primary 60E07, 60E10; Secondary 60B11, 60G51.

Key words and phrases: Hyperbolic characteristic functions, class L or SD probability distributions, selfdecomposability, Lévy process, Bessel squared process, Bessel bridge, local times.

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