O ct 2 00 6 Gamma Tilting Calculus for GGC and Dirichlet means withapplications to Linnik processes and Occupation Time Laws for

This paper explores various interfaces between the class of generalized gamma convolution (GGC) random variables, Dirichlet process mean functionals and phenomena connected to the local time and occupation time of p-skew Bessel processes and bridges discussed in Barlow, Pitman and Yor (1989), Pitman and Yor (1992, 1997b). First, some general calculus for GGC and Dirichlet process means func-tionals is developed. It then proceeds, via an investigation of positive Linnik random variables, and more generally random variables derived from compositions of a stable subordinator with GGC subordinators, to establish various distributional equivalences between these models and phenomena connected to local times and occupation times of what are defined as randomly skewed Bessel processes and bridges. This yields a host of interesting identities and explicit density formula for these models. Randomly skewed Bessel processes and bridges may be seen as a randomization of their p-skewed counterparts, and are shown to naturally arise via exponential tilting. As a special result it is shown that the occupation time of a p-skewed random Bessel process or (generalized) bridge is equivalent in distribution to the occupation time of a non-trivial randomly skewed process.