Quasi-Ergodic Limits for Moments of Jumps Under Absorbing Stable Processes

Daehong Kim () and Takara Tagawa ()
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Daehong Kim: Kumamoto University
Takara Tagawa: Kumamoto University

Journal of Theoretical Probability, 2025, vol. 38, issue 1, 1-19

Abstract: Abstract We study a quasi-ergodic theorem for moments of the mean-ratio of a discontinuous additive functional caused by the pure jump effects of an absorbing symmetric stable process on an open set $$D \subset \mathbb {R}^d$$ D ⊂ R d . Our result depends only on a simple geometric condition on D and does not require that the total mass of D is finite. As a result, we prove that the result holds if D is a subset of a horn-shaped region with the reference function satisfying some condition.

Keywords: Additive functionals; Compactness of killed semigroup; Horn-shaped region; Intrinsic ultracontractivity; Lévy system; Quasi-ergodic theorem; Primary 37A30; 60J45; Secondary 60G52; 47D06; 60J46 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-024-01380-y

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