My question is how to compute R(dx). But before I can ask that I have to write down the background to my problem, so bear withme
----------------------------------------------------------------------------
A tempered stable distribution is when a stable distribution is tempered by an exponential function of the form [latex]e^{-\theta{x}}[/latex]. In my particular case we are using a tempered stable law defined by Barndorff-Nielsen in the paper "modified stable processes" found here, http://economics.oul...nmsprocnew1.pdf.
In Barndorff's paper, , hence the tempering function is defined as .
In Rosinski's paper on "tempering stable processes" (which can be found http://www-m4.ma.tum.de/Papers/Rosinski/tstable.pd or http://citeseerx.ist.psu.edu/viewdoc...=rep1&type=pdf) he states that tempering of the stable density leads to tempering of the corresponding Levy measure , where .
Rosinski then goes on to say the Levy measure of a stable law in polar coordinates is of the form
and then says the Levy measure of a tempered stable density can be written as
he then says, the tempering function q in (2.2) can be represented as
Rosinski's paper also defines a measure R by
and has
now I know that for my particular tempered stable density the levy measure is given by
Rosinski then goes on to state Theorem 2.3: The Levy measure of a tempered stable distribution can be written in the form
----------------------------------------------------------------------
So the question is, how can I work out what is? and what is ?
-----------------------------------------------------------------------
I would greatly appreciate if anyone can help me on this one.