The central limit theorem for the Poisson shot-noise process
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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.
1984 ◽
Vol 21
(02)
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pp. 287-301
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1986 ◽
1987 ◽
Vol 24
(04)
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pp. 978-989
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2014 ◽
pp. 1224-1224