{
  "id": "1910.07464",
  "version": "v1",
  "published": "2019-10-16T16:39:30.000Z",
  "updated": "2019-10-16T16:39:30.000Z",
  "title": "Stationary solutions to the stochastic Burgers equation on the line",
  "authors": [
    "Alexander Dunlap",
    "Cole Graham",
    "Lenya Ryzhik"
  ],
  "comment": "43 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "We consider the stochastic Burgers equation on $\\mathbb{R}$, forced by the derivative of a noise that is white in time and colored in space. We show that, in a suitable space, there is a unique ergodic spacetime-stationary solution with any given mean. We also prove that the solution of the initial value problem with an initial condition that is an $L^1(\\mathbb{R})$-perturbation of a constant $a$ converges to the ergodic spacetime-stationary solution with mean $a$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-16T16:39:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "35R60"
    ],
    "keywords": [
      "stochastic burgers equation",
      "stationary solutions",
      "unique ergodic spacetime-stationary solution",
      "initial value problem",
      "initial condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}