Non-symmetric stable processes: Dirichlet heat kernel, Martin kernel and Yaglom limit

2023/10/12 by Leżaj, Łukasz
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2310.08570

Abstract

We study a d-dimensional non-symmetric strictly α-stable Lévy process X, whose spherical density is bounded and bounded away from the origin. First, we give sharp two-sided estimates on the transition density of X killed when leaving an arbitrary κ-fat set. We apply these results to get the existence of the Yaglom limit for arbitrary κ-fat cone. In the meantime we also obtain the spacial asymptotics of the survival probability at the vertex of the cone expressed by means of the Martin kernel for Γ and its homogeneity exponent. Our results hold for the dual process \widehatX, too.

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