• Corpus ID: 248834470

# Large-time and small-time behaviors of the spectral heat content for time-changed stable processes

@inproceedings{Kobayashi2022LargetimeAS,
title={Large-time and small-time behaviors of the spectral heat content for time-changed stable processes},
author={Kei Kobayashi and Hyunchul Park},
year={2022}
}
• Published 17 May 2022
• Mathematics
We study the large-time and small-time asymptotic behaviors of the spectral heat content for time-changed stable processes, where the time change belongs to a large class of inverse subordinators. For the large-time behavior, the spectral heat content decays polynomially with the decay rate determined by the Laplace exponent of the underlying subordinator, which is in sharp contrast to the exponential decay observed in the case when the time change is a subordinator. On the other hand, the…

## References

SHOWING 1-10 OF 13 REFERENCES
Spectral heat content for time-changed killed Brownian motions
• Mathematics
• 2020
The spectral heat content is investigated for time-changed killed Brownian motions on C1,1 open sets, where the time change is given by either a subordinator or an inverse subordinator, with the
Small time asymptotics of spectral heat contents for subordinate killed Brownian motions related to isotropic α ‐stable processes
• Mathematics
Bulletin of the London Mathematical Society
• 2019
In this paper, we study the small time asymptotic behavior of the spectral heat content Q∼D(α)(t) of an arbitrary bounded C1,1 domain D with respect to the subordinate killed Brownian motion in D via
Higher order terms of spectral heat content for killed subordinate and subordinate killed Brownian motions related to symmetric \alpha-stable processes in R
We investigate the 3rd term of spectral heat content for killed subordinate and subordinate killed Brownian motions on a bounded open interval D = (a, b) in a real line when the underlying
Spectral heat content for α-stable processes in C1,1 open sets
• Mathematics
Electronic Journal of Probability
• 2022
In this paper we study the asymptotic behavior, as t ↓ 0, of the spectral heat content Q D (t) for isotropic α-stable processes, α ∈ [1, 2), in bounded C open sets D ⊂ R, d ≥ 2. Together with the
Heat content for stable processes in domains of $\R^d$
This paper studies the small time behavior of the heat content of rotationally invariant $\alpha$--stable processes, $0<\alpha \leq 2$, in domains in $\R^d$. Unlike the asymptotics for the heat
Lévy processes and infinitely divisible distributions
Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5.
Stochastic Models for Fractional Calculus
• Mathematics
• 2011
Preface: 1 Introduction 1.1 The traditional diffusion model 1.2 Fractional diffusion 2 Fractional Derivatives 2.1 The Grunwald formula 2.2 More fractional derivatives 2.3 The Caputo derivative 2.4