Open Access
February, 1991 Loud Shot Noise
R. A. Doney, George L. O'Brien
Ann. Appl. Probab. 1(1): 88-103 (February, 1991). DOI: 10.1214/aoap/1177005982

Abstract

We consider problems involving large or loud values of the shot noise process X(t):=i:τith(tτi),t0, where h:[0,)[0,) is nonincreasing and (τi,i0) is the sequence of renewal times of a renewal process. Results are obtained by extending the renewal sequence to all iZ and considering the stationary sequence (ξn) given by ξn=inh(τnτi). We show that ξn has a thin tail in the sense that under broad circumstances Pr{ξn>x+δξn>x}0 as x, where δ>0. We also show that Pr{max(ξ1,,ξn)un}(Pr{ξ0un})n0 for real sequences (un) for which limsupnPr{ξ0>un}<.

Citation

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R. A. Doney. George L. O'Brien. "Loud Shot Noise." Ann. Appl. Probab. 1 (1) 88 - 103, February, 1991. https://doi.org/10.1214/aoap/1177005982

Information

Published: February, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0724.60105
MathSciNet: MR1097465
Digital Object Identifier: 10.1214/aoap/1177005982

Subjects:
Primary: 60K99
Secondary: 60J05 , 60K05

Keywords: Extreme values , renewal processes , Shot noise

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.1 • No. 1 • February, 1991
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