{
  "id": "2111.07293",
  "version": "v2",
  "published": "2021-11-14T09:35:36.000Z",
  "updated": "2022-12-11T11:08:14.000Z",
  "title": "Weak Uniqueness for the Stochastic Heat Equation Driven by a Multiplicative Stable Noise",
  "authors": [
    "Sayantan Maitra"
  ],
  "comment": "31 pages, 1 figure. Corrected an error from the previous version. The main result now incorporates a larger class of initial conditions",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the stochastic heat equation $$\\frac{\\partial Y_t(x)}{\\partial t} = \\frac{1}{2} \\Delta_x Y_t(x) + Y_{t-}(x)^{\\beta} \\dot{L}^{\\alpha}$$ with $t \\ge 0$, $x \\in \\mathbb{R}$ and $L^{\\alpha}$ being an $\\alpha$-stable white noise without negative jumps. Under appropriate non-negative initial conditions, when $\\alpha \\in (1,2)$ and $\\beta \\in (\\frac{1}{\\alpha}, 1)$ we prove that weak uniqueness holds for the above using the approximating duality approach developed by Mytnik (Ann. Probab. (1998) 26 968-984).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-12-11T11:08:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15"
    ],
    "keywords": [
      "stochastic heat equation driven",
      "multiplicative stable noise",
      "weak uniqueness holds",
      "appropriate non-negative initial conditions",
      "stable white noise"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}