A TECHNIQUE FOR COMPUTING THE PDFS AND CDFS OF NONNEGATIVE INFINITELY DIVISIBLE RANDOM VARIABLES

作者：Veillette Mark S^*; Ta**u Murad S

来源：Journal of Applied Probability, 2011, 48(1): 217-237.

• Infinitely divisible distribution
• Post-Widder formula
• stable distribution
• stochastic integration

We present a method for computing the probability density PDF) and the cumulative distribution CDF) of a nonnegative infinitely divisible random variable X. Our method uses the Levy-Khintchine representation of the Laplace transform Ee(-lambda X) = e(-phi(lambda)) where phi 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 Levy processes.

• 出版日期2011-3