{
  "id": "2306.11690",
  "version": "v1",
  "published": "2023-06-20T17:09:20.000Z",
  "updated": "2023-06-20T17:09:20.000Z",
  "title": "A unified approach to the small-time behavior of the spectral heat content for isotropic Lévy processes",
  "authors": [
    "Kei Kobayashi",
    "Hyunchul Park"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper establishes the precise small-time asymptotic behavior of the spectral heat content for isotropic L\\'evy processes on bounded $C^{1,1}$ open sets of $\\mathbb{R}^{d}$ with $d\\ge 2$, where the underlying characteristic exponents are regularly varying at infinity with index $\\alpha\\in (1,2]$, including the case $\\alpha=2$. Moreover, this asymptotic behavior is shown to be stable under an integrable perturbation of its L\\'evy measure. These results cover a wide class of isotropic L\\'evy processes, including Brownian motions, stable processes, and jump diffusions, and the proofs provide a unified approach to the asymptotic behavior of the spectral heat content for all of these processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-20T17:09:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectral heat content",
      "isotropic lévy processes",
      "unified approach",
      "small-time behavior",
      "isotropic levy processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}