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

نویسنده

  • Lancelot F. James
چکیده

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.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples

• In Section 1, we present a number of classical results concerning the Generalized Gamma Convolution ( : GGC) variables, their Wiener-Gamma representations, and relation with the Dirichlet processes. • To a GGC variable, one may associate a unique Thorin measure. Let G a positive r.v. and Γt(G) ( resp. Γt(1/G) ) the Generalized Gamma Convolution with Thorin measure t-times the law of G (resp. ...

متن کامل

ar X iv : m at h / 06 04 08 6 v 2 [ m at h . ST ] 6 A pr 2 00 6 Laws and Likelihoods for Ornstein Uhlenbeck - Gamma and other BNS

In recent years there have been many proposals as flexible alternatives to Gaussian based continuous time stochastic volatility models. A great deal of these models employ positive Lévy processes. Among these are the attractive non-Gaussian positive Ornstein-Uhlenbeck (OU) processes proposed by Barndorff-Nielsen and Shephard (BNS) in a series of papers. One current problem of these approaches i...

متن کامل

ar X iv : m at h / 06 04 08 6 v 1 [ m at h . ST ] 5 A pr 2 00 6 Laws and Likelihoods for Ornstein Uhlenbeck - Gamma and other BNS

In recent years there have been many proposals as flexible alternatives to Gaussian based continuous time stochastic volatility models. A great deal of these models employ positive Lévy processes. Among these are the attractive non-Gaussian positive Ornstein-Uhlenbeck (OU) processes proposed by Barndorff-Nielsen and Shephard (BNS) in a series of papers. One current problem of these approaches i...

متن کامل

Lamperti Type Laws: Positive Linnik, Bessel Bridge Occupation and Mittag-Leffler Functions

This paper explores various distributional aspects of random variables defined as the ratio of two independent positive random variables where one variable has an α stable law, for 0 < α < 1, and the other variable has the law defined by polynomially tilting the density of an α stable random variable by a factor θ > −α. When θ = 0, these variables equate with the ratio investigated by Lamperti ...

متن کامل

In nitely divisible laws associated with hyperbolic functions

The in nitely divisible distributions on R+ of random variables Ct, St and Tt with Laplace transforms 1 cosh p 2 t ; p 2 sinh p 2 !t ; and tanh p 2 p 2 !t respectively are characterized for various t > 0 in a number of di erent ways: by simple relations between their moments and cumulants, by corresponding relations between the distributions and their L evy measures, by recursions for their Mel...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2006