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Tail asymptotics for exponential functionals of Lévy processes: The convolution equivalent case

Víctor Rivero (2012)

Annales de l'I.H.P. Probabilités et statistiques

We determine the rate of decrease of the right tail distribution of the exponential functional of a Lévy process with a convolution equivalent Lévy measure. Our main result establishes that it decreases as the right tail of the image under the exponential function of the Lévy measure of the underlying Lévy process. The method of proof relies on fluctuation theory of Lévy processes and an explicit pathwise representation of the exponential functional as the exponential functional of a bivariate subordinator....

Variance of periodic measure of bounded set with random position

Jiří Janáček (2006)

Commentationes Mathematicae Universitatis Carolinae

The principal term in the asymptotic expansion of the variance of the periodic measure of a ball in d under uniform random shift is proportional to the ( d + 1 ) st power of the grid scaling factor. This result remains valid for a bounded set in d with sufficiently smooth isotropic covariogram under a uniform random shift and an isotropic rotation, and the asymptotic term is proportional also to the ( d - 1 ) -dimensional measure of the object boundary. The related coefficients are calculated for various periodic...

Vector-valued Choquet-Deny theorem, renewal equation and self-similar measures

Ka-Sing Lau, Jian-Rong Wang, Cho-Ho Chu (1995)

Studia Mathematica

The Choquet-Deny theorem and Deny’s theorem are extended to the vector-valued case. They are applied to give a simple nonprobabilistic proof of the vector-valued renewal theorem, which is used to study the L p -dimension, the L p -density and the Fourier transformation of vector-valued self-similar measures. The results answer some questions raised by Strichartz.

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