On the one--dimensional spectral Heat content for stable processes

TL;DR

This paper derives the second term in the small-time asymptotic expansion of the spectral heat content for one-dimensional stable processes, revealing connections to the distribution of extremal process values.

Contribution

It provides the second-order term in the spectral heat content expansion for stable processes, advancing understanding of their small-time behavior.

Findings

Derived the second term in the asymptotic expansion

Linked spectral heat content to extremal process distributions

Enhanced understanding of stable process heat content behavior

Abstract

This paper provides the second term in the small time asymptotic expansion of the spectral heat content of a rotationally invariant $\alpha$--stable process, $0<\alpha \leq 2$, for the interval $(a,b)$. The small time behavior of the spectral heat content turns out to be linked to the distribution of the supremum and infimum processes.