학술논문
Distribution Functions of Poisson Random Integrals: Analysis and Computation.
Document Type
Article
Author
Source
Subject
*Distribution (Probability theory)
*Statistical sampling
*Stochastic processes
Poisson processes
Kernel functions
Finite differences
Numerical analysis
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Language
ISSN
1387-5841
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. [ABSTRACT FROM AUTHOR]