Distribution functions of Poisson random integrals: analysis and computation
Taqqu, Murad S.
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Citation (published version)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
We want to compute the cumulative distribution function of a one-dimensional Poisson stochastic integral 𝐼(𝑔)=∫𝑇0𝑔(𝑠)𝑁(𝑑𝑠) , where N is a Poisson random measure with control measure n and g is a suitable kernel function. We do so by combining a Kolmogorov–Feller 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.