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Spectral heat content for Lévy processes

Author

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  • Tomasz Grzywny
  • Hyunchul Park
  • Renming Song

Abstract

In this paper we study the spectral heat content for various Lévy processes. We establish the small time asymptotic behavior of the spectral heat content for Lévy processes of bounded variation in Rd, d≥1. We also study the spectral heat content for arbitrary open sets of finite Lebesgue measure in R with respect to symmetric Lévy processes of unbounded variation under certain conditions on their characteristic exponents. Finally, we establish that the small time asymptotic behavior of the spectral heat content is stable under integrable perturbations to the Lévy measure.

Suggested Citation

  • Tomasz Grzywny & Hyunchul Park & Renming Song, 2019. "Spectral heat content for Lévy processes," Mathematische Nachrichten, Wiley Blackwell, vol. 292(4), pages 805-825, April.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:4:p:805-825
    DOI: 10.1002/mana.201800035
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    Cited by:

    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. 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).

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