On level and collision sets of some Feller processes
Abstract
This paper is about lower and upper bounds for the Hausdorff dimension of the level and collision sets of a class of Feller processes. Our approach is motivated by analogous results for L\'evy processes by Hawkes (for level sets), Taylor and Jain & Pruitt (for collision sets). Since Feller processes lack independent or stationary increments, the methods developed for L\'evy processes cannot be used in a straightforward manner. Under the assumption that the Feller process possesses a transition probability density, which admits lower and upper bounds of a certain type, we derive sufficient conditions for regularity and non-polarity of points; together with suitable time changes this allows us to get upper and lower bounds for the Hausdorff dimension.
Keywords
Cite
@article{arxiv.1412.8726,
title = {On level and collision sets of some Feller processes},
author = {Victoria Knopova and René L. Schilling},
journal= {arXiv preprint arXiv:1412.8726},
year = {2015}
}