{
  "id": "1804.03622",
  "version": "v2",
  "published": "2018-04-10T16:49:37.000Z",
  "updated": "2018-12-20T01:10:09.000Z",
  "title": "Small time asymptotics of spectral heat contents for subordinate killed Brownian motions related to isotropic α-stable processes",
  "authors": [
    "Hyunchul Park",
    "Renming Song"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we study the small time asymptotic behavior of the spectral heat content $\\widetilde{Q}_D^{(\\alpha)}(t)$ of an arbitrary bounded $C^{1,1}$ domain $D$ with respect to the \\textit{subordinate killed Brownian motion} in $D$ via an $(\\alpha/2)$-stable subordinator. For all $\\alpha\\in (0,2)$, we establish a two-term small time expansion for $\\widetilde{Q}_D^{(\\alpha)}(t)$ in all dimensions. When $\\alpha\\in (1,2)$ and $d\\geq 2$, we establish a three-term small time expansion for $\\widetilde{Q}_D^{(\\alpha)}(t)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2018-12-20T01:10:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "subordinate killed brownian motions",
      "spectral heat content",
      "two-term small time expansion",
      "small time asymptotic behavior",
      "three-term small time expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}