A technique for computing the PDFs and CDFs of nonnegative infinitely divisible random variables

Veillette, Mark S.; Taqqu, Murad S.

J. Appl. Probab., Tome 48 (2011) no. 1, p. 217-237 / Harvested from Project Euclid

Résumé

We present a method for computing the probability density function (PDF) and the cumulative distribution function (CDF) of a nonnegative infinitely divisible random variable X. Our method uses the Lévy-Khintchine representation of the Laplace transform Ee^-λX = e^-ϕ(λ), where ϕ is the Laplace exponent. 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 nonnegative Lévy processes.

Publié le : 2011-03-15
Classification: Infinitely divisible distribution, Post-Widder formula, stable distribution, stochastic integration, 60E07, 65C50, 60-08, 60-04

@article{1300198146,
     author = {Veillette, Mark S. and Taqqu, Murad S.},
     title = {A technique for computing the PDFs and CDFs of nonnegative infinitely divisible random variables},
     journal = {J. Appl. Probab.},
     volume = {48},
     number = {1},
     year = {2011},
     pages = { 217-237},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1300198146}
}

Veillette, Mark S.; Taqqu, Murad S. A technique for computing the PDFs and CDFs of nonnegative infinitely divisible random variables. J. Appl. Probab., Tome 48 (2011) no. 1, pp.  217-237. http://gdmltest.u-ga.fr/item/1300198146/