Stochastic integral characterizations of semi-selfdecomposable distributions and related Ornstein-Uhlenbeck type processes
Abstract
In this paper, three topics on semi-selfdecomposable distributions are studied. The first one is to characterize semi-selfdecomposable distributions by stochastic integrals with respect to Levy processes. This characterization defines a mapping from an infinitely divisible distribution with finite log-moment to a semi-selfdecomposable distribution. The second one is to introduce and study a Langevin type equation and the corresponding Ornstein-Uhlenbecktype process whose limiting distribution is semi-selfdecomposable. Also, semi-stationary Ornstein-Uhlenbeck type processes with semi-selfdecomposable distributions are constructed. The third one is to study the iteration of the mapping above. The iterated mapping is expressed as a single mapping with a different integrand. Also, nested subclasses of the class of semi-selfdecomposable distributions are considered, andit is shown that the limit of these nested subclasses is the closure of the class of semi-stable distributions.
Keywords
Cite
@article{arxiv.0911.3449,
title = {Stochastic integral characterizations of semi-selfdecomposable distributions and related Ornstein-Uhlenbeck type processes},
author = {Makoto Maejima and Yohei Ueda},
journal= {arXiv preprint arXiv:0911.3449},
year = {2009}
}