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

Łukasz Leżaj

Stochastic Processes and their Applications, 2024, vol. 174, issue C

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 X̂, too.

Keywords: Non-symmetric stable process; Heat kernel estimates; Dirichlet problem; Yaglom limit; Martin kernel (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104362

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