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

Author

Listed:
  • Daehong Kim

    (Kumamoto University)

  • Takara Tagawa

    (Kumamoto University)

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.

Suggested Citation

  • Daehong Kim & Takara Tagawa, 2025. "Quasi-Ergodic Limits for Moments of Jumps Under Absorbing Stable Processes," Journal of Theoretical Probability, Springer, vol. 38(1), pages 1-19, March.
    • Handle: RePEc:spr:jotpro:v:38:y:2025:i:1:d:10.1007_s10959-024-01380-y
    DOI: 10.1007/s10959-024-01380-y
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    References listed on IDEAS

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    1. Masayoshi Takeda, 2019. "Existence and Uniqueness of Quasi-stationary Distributions for Symmetric Markov Processes with Tightness Property," Journal of Theoretical Probability, Springer, vol. 32(4), pages 2006-2019, December.
    2. Breyer, L. A. & Roberts, G. O., 1999. "A quasi-ergodic theorem for evanescent processes," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 177-186, December.
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