Hitting properties and non-uniqueness for SDE driven by stable processes
Probability
2011-11-24 v2
Abstract
We study a class of self-similar jump type SDEs driven by H\"older-continuous drift and noise coefficients. Using the Lamperti transformation for positive self-similar Markov processes we obtain a necessary and sufficient condition for almost sure extinction in finite time. We then show that for certain parameters pathwise uniqueness holds in a restricted sense, namely among solutions spending a Lebesgue-negligible amount of time at 0. A direct power transformation plays a key role.
Cite
@article{arxiv.1111.4388,
title = {Hitting properties and non-uniqueness for SDE driven by stable processes},
author = {Julien Berestycki and Leif Doering and Leonid Mytnik and Lorenzo Zambotti},
journal= {arXiv preprint arXiv:1111.4388},
year = {2011}
}