Distribution Functions of Poisson Random Integrals: Analysis and Computation

Mark Veillette and Murad S. Taqqu ()
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Mark Veillette: Boston University
Murad S. Taqqu: Boston University

Methodology and Computing in Applied Probability, 2012, vol. 14, issue 2, 169-202

Abstract: Abstract We want to compute the cumulative distribution function of a one-dimensional Poisson stochastic integral $I(g) = \displaystyle \int_0^T g(s) N(ds)$ , 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.

Keywords: Poisson integrals; CDFs; Finite-difference scheme; Kolmogorov–Feller equations; Primary 60-08, 60H05, 65L12; Secondary 60G55 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-010-9195-6

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