On the shape of the ground state eigenfunction for stable processes
Probability
2007-05-23 v1
Abstract
We prove that the ground state eigenfunction for symmetric stable processes of order killed upon leaving the interval is concave on . We call this property "mid--concavity." A similar statement holds for rectangles in , . These result follow from similar results for finite dimensional distributions of Brownian motion and subordination.
Cite
@article{arxiv.math/0407260,
title = {On the shape of the ground state eigenfunction for stable processes},
author = {Rodrigo Banuelos and Tadeusz Kulczycki and Pedro J. Mendez-Hernandez},
journal= {arXiv preprint arXiv:math/0407260},
year = {2007}
}