Subdiagonal and almost uniform distributions.
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....
The space of distribution functions endowed with the metric introduced in [5] is separable.
The principal term in the asymptotic expansion of the variance of the periodic measure of a ball in under uniform random shift is proportional to the st power of the grid scaling factor. This result remains valid for a bounded set in with sufficiently smooth isotropic covariogram under a uniform random shift and an isotropic rotation, and the asymptotic term is proportional also to the -dimensional measure of the object boundary. The related coefficients are calculated for various periodic...
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 -dimension, the -density and the Fourier transformation of vector-valued self-similar measures. The results answer some questions raised by Strichartz.