On the Shape of the Ground State Eigenfunction for Stable Processes
نویسنده
چکیده
We prove that the ground state eigenfunction for symmetric stable processes of order α ∈ (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 > 1. These result follow from similar results for finite dimensional distributions of Brownian motion and subordination.
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تاریخ انتشار 2004