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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

A conjecture on the behavior of tails of fixed points of the shot noise transform


Author: O. M. Iksanov
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 69 (2003).
Journal: Theor. Probability and Math. Statist. 69 (2004), 55-60
MSC (2000): Primary 60E07; Secondary 40E05
Published electronically: February 7, 2005
MathSciNet review: 2110904
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Abstract | References | Similar Articles | Additional Information

Abstract: We show, under some restrictions on the response function depending on a parameter $\alpha$, that the tails of fixed points of transforms of a Poisson shot noise process are proportional at infinity to the exponential function of order $-\alpha$ if $\alpha\in(1,2)$. We advance an argument in support of the conjecture that this result remains true for $\alpha\geq 2$.


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Additional Information

O. M. Iksanov
Affiliation: Faculty for Cybernetics, Kyiv Taras Shevchenko National University, Kyiv 01033, Ukraine
Email: iksan@unicyb.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-05-00613-7
PII: S 0094-9000(05)00613-7
Received by editor(s): November 14, 2002
Published electronically: February 7, 2005
Article copyright: © Copyright 2005 American Mathematical Society