Murad S. Taqqu (Université de Boston) sera en visite durant le mois de juin 2011.
Il donnera un séminaire le mardi 14 juin à 16h15 en amphi Saphir.
Technique for computing the PDFs and CDFs of non-negative infinitely divisible random variables
Infinitely divisible distributions appear in many fields,
including finance. They include the normal, chi-square,
Poisson, compound Poisson and limits thereof,
as well as infinite variance stable distributions.
I will present an efficient method for computing
the probability density function (PDF) and cumulative
distribution function (CDF) of non-negative infinitely divisible random variables.
This method uses the Levy-Khintchine representation
of the Laplace transform of the distribution.
We apply the Post-Widder method for Laplace transform
inversion combined with a sequence convergence accelerator to obtain
accurate results. We demonstrate this technique on several examples
including the stable distribution, mixtures thereof, and integrals
with respect to non-negative Poisson and Levy processes.
This is joint work with Mark S. Veillette.
The article can be downloaded from arxiv: