On convolution equivalence with applications
Qihe Tang
Source: Bernoulli Volume 12, Number 3 (2006), 535-549.
Abstract
A distribution on is said to belong to the class for some if holds for all and exists and is finite. Let and be two independent random variables, where has a distribution in the class and is non-negative with an endpoint . We prove that the product has a distribution in the class . We further apply this result to investigate the tail probabilities of Poisson shot noise processes and certain stochastic equations with random coefficients.
Keywords: asymptotics; class \mathcal{S}(γ); endpoint; Poisson shot noise; rapid variation; stochastic equation; uniformity
Full-text: Open access
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Permanent link to this document: http://projecteuclid.org/euclid.bj/1151525135
Digital Object Identifier: doi:10.3150/bj/1151525135
Mathematical Reviews number (MathSciNet):
MR2232731
Zentralblatt MATH identifier:
1114.60015
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