{
  "id": "1705.00422",
  "version": "v1",
  "published": "2017-05-01T05:46:16.000Z",
  "updated": "2017-05-01T05:46:16.000Z",
  "title": "$L_2$-Small Deviations for Weighted Stationary Processes",
  "authors": [
    "Mikhail Lifshits",
    "Alexander Nazarov"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We find logarithmic asymptotics of $L_2$-small deviation probabilities for weighted stationary Gaussian processes (both for real and complex-valued) having power-type discrete or continuous spectrum. As in the recent work by Hong, Lifshits and Nazarov, our results are based on the spectral theory of pseudo-differential operators developed by Birman and Solomyak.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-01T05:46:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60G10",
      "60G22",
      "47G30"
    ],
    "keywords": [
      "weighted stationary processes",
      "small deviation probabilities",
      "weighted stationary gaussian processes",
      "logarithmic asymptotics",
      "power-type discrete"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}