Gamma Tilting Calculus for GGC and Dirichlet means with applications to Linnik processes and Occupation Time Laws for Randomly Skewed Bessel Processes and Bridges

Details Gamma Tilting Calculus for GGC and Dirichlet means with applications to Linnik processes and Occupation Time Laws for Randomly Skewed Bessel Processes and Bridges Gamma Tilting Calculus for GGC and Dirichlet means with applications to Linnik processes and Occupation Time Laws for Randomly Skewed Bessel Processes and Bridges

2006-10-06

arxiv.org/abs/math/0610218v3

Mathematics

Probability

Corrections made to Proposition 5.15 and Remark 25. Additional typos corrected

Scientific paper

This paper develops some general calculus for GGC and Dirichlet process means functionals. 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 developed in Barlow, Pitman and Yor (1989) and Pitman and Yor (1997), 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.

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