Small noise asymptotics and first passage times of integrated Ornstein-Uhlenbeck processes driven by $\alpha$-stable L\'{e}vy processes
Probability
2014-02-06 v2
Abstract
In this paper, we study the asymptotic behaviour of one-dimensional integrated Ornstein-Uhlenbeck processes driven by -stable L\'{e}vy processes of small amplitude. We prove that the integrated Ornstein-Uhlenbeck process converges weakly to the underlying -stable L\'{e}vy process in the Skorokhod -topology which secures the weak convergence of first passage times. This result follows from a more general result about approximations of an arbitrary L\'{e}vy process by continuous integrated Ornstein-Uhlenbeck processes in the -topology.
Keywords
Cite
@article{arxiv.1205.6116,
title = {Small noise asymptotics and first passage times of integrated Ornstein-Uhlenbeck processes driven by $\alpha$-stable L\'{e}vy processes},
author = {Robert Hintze and Ilya Pavlyukevich},
journal= {arXiv preprint arXiv:1205.6116},
year = {2014}
}
Comments
Published in at http://dx.doi.org/10.3150/12-BEJ485 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)