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A unified approach to the small-time behavior of the spectral heat content for isotropic Lévy processes

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  • Kobayashi, Kei
  • Park, Hyunchul

Abstract

This paper establishes the precise small-time asymptotic behavior of the spectral heat content for isotropic Lévy processes on bounded C1,1 open sets of Rd with d≥2, where the underlying characteristic exponents are regularly varying at infinity with index α∈(1,2], including the case α=2. Moreover, this asymptotic behavior is shown to be stable under an integrable perturbation of its Lévy measure. These results cover a wide class of isotropic Lévy processes, including Brownian motions, stable processes, and jump diffusions, and the proofs provide a unified approach to the asymptotic behavior of the spectral heat content for all of these processes.

Suggested Citation

  • Kobayashi, Kei & Park, Hyunchul, 2024. "A unified approach to the small-time behavior of the spectral heat content for isotropic Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:spapps:v:171:y:2024:i:c:s0304414924000371
    DOI: 10.1016/j.spa.2024.104331
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    References listed on IDEAS

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    1. Kei Kobayashi & Hyunchul Park, 2023. "Spectral Heat Content for Time-Changed Killed Brownian Motions," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1148-1180, June.
    2. Tomasz Grzywny & Hyunchul Park & Renming Song, 2019. "Spectral heat content for Lévy processes," Mathematische Nachrichten, Wiley Blackwell, vol. 292(4), pages 805-825, April.
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    1. Kei Kobayashi & Hyunchul Park, 2023. "Spectral Heat Content for Time-Changed Killed Brownian Motions," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1148-1180, June.

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