Spectral Heat Content for Time-Changed Killed Brownian Motions

Kei Kobayashi () and Hyunchul Park ()
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Kei Kobayashi: Fordham University, The Bronx
Hyunchul Park: State University of New York at New Paltz

Journal of Theoretical Probability, 2023, vol. 36, issue 2, 1148-1180

Abstract: 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 ) .

Keywords: Spectral heat content; Subordinate killed Brownian motions; Subordinator; Inverse subordinator; 60G51; 60K50 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-022-01188-8

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