On the shape of the ground state eigenfunction for stable processes

Details On the shape of the ground state eigenfunction for stable processes On the shape of the ground state eigenfunction for stable processes

2004-07-15

arxiv.org/abs/math/0407260v1

Mathematics

Probability

Scientific paper

We prove that the ground state eigenfunction for symmetric stable processes of order $\alpha\in (0, 2)$ killed upon leaving the interval $(-1, 1)$ is concave on $(-{1/2}, {1/2})$. We call this property "mid--concavity." A similar statement holds for rectangles in $\R^d$, $d>1$. These result follow from similar results for finite dimensional distributions of Brownian motion and subordination.

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