{
  "annotation_id": "8961203e-2560-4d59-a8f5-d5181849ac21",
  "date_created": "2026-03-02T18:00:49.375000Z",
  "date_modified": "2026-03-02T18:00:49.375000Z",
  "file_hash": "6400340e050597ef4f666d4638c66136bde9e917c14e263f7d5dc731570d3d45",
  "private": false,
  "record": {
    "abstract": "It is common for scale-dependent analysis of stochastic data to use the\nincrement $\\Delta(t,r) = \\xi(t+r) - \\xi(t)$ of a data set $\\xi(t)$ as a\nstochastic measure, where $r$ denotes the scale. For joint statistics of\n$\\Delta(t,r)$ and $\\Delta(t,r\u0027)$ the question how to nest the increments on\ndifferent scales $r,r\u0027$ is investigated. Here we show that in some cases\nspurious correlations between scales can be introduced by the common\nleft-justified definition. The consequences for a Markov process are discussed.\nThese spurious correlations can be avoided by an appropriate nesting of\nincrements. We demonstrate this effect for different data sets and show how it\ncan be detected and quantified. The problem allows to propose a unique method\nto distinguish between experimental data generated by a noiselike or a\nLangevin-like random-walk process, respectively.",
    "arxiv_id": "physics/0404021",
    "authors": [
      "Matthias Waechter",
      "Alexei Kouzmitchev",
      "Joachim Peinke"
    ],
    "categories": [
      "physics.data-an",
      "cond-mat.dis-nn"
    ],
    "doi": "10.1103/PhysRevE.70.055103",
    "journal_ref": "Physical Review E 70, 055103 (2004)",
    "title": "Increment definitions for scale dependent analysis of stochastic data",
    "url": "https://arxiv.org/abs/physics/0404021"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "996782d6-dec8-45fb-89c4-e45e7fff2b11",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}