{
  "id": "2305.19239",
  "version": "v1",
  "published": "2023-05-30T17:28:50.000Z",
  "updated": "2023-05-30T17:28:50.000Z",
  "title": "Characterization of p-exponents by continuous wavelet transforms, applications to the multifractal analysis of sum of random pulses",
  "authors": [
    "Guillaume Saës"
  ],
  "categories": [
    "math.CA",
    "cs.NA",
    "math.FA",
    "math.NA"
  ],
  "abstract": "The theory of orthonormal wavelet bases is a useful tool in multifractal analysis, as it provides a characterization of the different exponents of pointwise regularities (H{\\\"o}lder, p-exponent, lacunarity, oscillation, etc.). However, for some homogeneous self-similar processes, such as sums of random pulses (sums of regular, well-localized functions whose expansions and translations are random), it is easier to estimate the spectrum using continuous wavelet transforms. In this article, we present a new characterization of p-exponents by continuous wavelet transforms and we provide an application to the regularity analysis of sums of random pulses.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-30T17:28:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuous wavelet transforms",
      "random pulses",
      "multifractal analysis",
      "characterization",
      "p-exponent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}