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
DOI:
https://doi.org/10.1090/S0094-9000-05-00613-7
Published electronically:
February 7, 2005
MathSciNet review:
2110904
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We show, under some restrictions on the response function depending on a parameter , that the tails of fixed points of transforms of a Poisson shot noise process are proportional at infinity to the exponential function of order
if
. We advance an argument in support of the conjecture that this result remains true for
.
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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:
https://doi.org/10.1090/S0094-9000-05-00613-7
Received by editor(s):
November 14, 2002
Published electronically:
February 7, 2005
Article copyright:
© Copyright 2005
American Mathematical Society