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The central limit theorem for the Poisson shot-noise process

Published online by Cambridge University Press:  14 July 2016

John A. Lane
John A. Lane*
Affiliation:
University College of Wales, Aberystwyth
*
∗ Postal address: Department of Statistics, University College of Wales, Penglais, Aberystwyth, SY23 3DB, Wales.
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Abstract

The Poisson shot-noise process discussed here takes the form f:oo H(t, s)N(ds), where N(· is the counting measure of a Poisson process and the H(·, s) are independent stochastic processes. Necessary and sufficient conditions are obtained for convergence in distribution, as t ∼ OC, to any infinitely divisible distribution. The main interest is in the explosive transient one-sided shot-noise, Y(t) = f:1 H(t, s)N(ds) where Var Y(t)∼ oc, Here conditions for asymptotic normality are discussed in detail. Important examples include the Poisson cluster point process and the integrated stationary shotnoise.

Keywords

INFINITE DIVISIBILITYFELLER CANONICAL MEASUREASYMPTOTIC NORMALITYCLUSTER POINT PROCESSINTEGRATED SHOT-NOISE
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 2 , June 1984 , pp. 287 - 301
Copyright
Copyright © Applied Probability Trust 1984 

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Footnotes

The major part of this work was carried out while the author was a Ph.D. student in the Department of Mathematics, Imperial College of Science and Technology, London.

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