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: probability distributions or Lévy class of probability laws).
Consequently, they admit associated background driving Lévy processes Y (BDLP’s Y). We
interpret the distributions of 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 or
probability distributions, selfdecomposability, Lévy process, Bessel squared process, Bessel
bridge, local times.