English

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 α(0,2)\alpha\in (0, 2) killed upon leaving the interval (1,1)(-1, 1) is concave on (1/2,1/2)(-{1/2}, {1/2}). We call this property "mid--concavity." A similar statement holds for rectangles in Rd\R^d, d>1d>1. 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}
}