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Spectral Heat Content for Time-Changed Killed Brownian Motions

Author

Listed:
  • Kei Kobayashi

    (Fordham University, The Bronx)

  • Hyunchul Park

    (State University of New York at New Paltz)

Abstract

The spectral heat content is investigated for time-changed killed Brownian motions on $$C^{1,1}$$ C 1 , 1 open sets, where the time change is given by either a subordinator or an inverse subordinator, with the underlying Laplace exponent being regularly varying at $$\infty $$ ∞ with index $$\beta \in (0,1)$$ β ∈ ( 0 , 1 ) . In the case of inverse subordinators, the asymptotic limit of the spectral heat content in small time is shown to involve a probabilistic term depending only on $$\beta \in (0,1)$$ β ∈ ( 0 , 1 ) . In contrast, in the case of subordinators, this universality holds only when $$\beta \in (\frac{1}{2}, 1)$$ β ∈ ( 1 2 , 1 ) .

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:2:d:10.1007_s10959-022-01188-8
    DOI: 10.1007/s10959-022-01188-8
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    References listed on IDEAS

    as
    1. Kobayashi, Kei, 2016. "Small ball probabilities for a class of time-changed self-similar processes," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 155-161.
    2. Magdziarz, Marcin, 2009. "Stochastic representation of subdiffusion processes with time-dependent drift," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3238-3252, October.
    3. 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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    Cited by:

    1. 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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