Distribution functions of Poisson random integrals: analysis and computation
Files
First author draft
Date
2012-06-01
Authors
Veillette, Mark
Taqqu, Murad S.
Version
First author draft
OA Version
Citation
Mark Veillette, Murad S Taqqu. 2012. "Distribution Functions of Poisson Random Integrals: Analysis and Computation." METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, Volume 14, Issue 2, pp. 169 - 202 (34). https://doi.org/10.1007/s11009-010-9195-6
Abstract
We want to compute the cumulative distribution function of a one-dimensional Poisson stochastic integral ๐ผ(๐)=โซ๐0๐(๐ )๐(๐๐ ) , where N is a Poisson random measure with control measure n and g is a suitable kernel function. We do so by combining a KolmogorovโFeller equation with a finite-difference scheme. We provide the rate of convergence of our numerical scheme and illustrate our method on a number of examples. The software used to implement the procedure is available on demand and we demonstrate its use in the paper.