{
  "annotation_id": "7703782e-1e6e-414e-b936-bc64ed9f3a11",
  "date_created": "2026-03-02T18:01:11.527000Z",
  "date_modified": "2026-03-02T18:01:11.527000Z",
  "file_hash": "b0fc24689ddc3c0732ffb56bafb335e3ac06510b2f09f79e6360f85820fa2767",
  "private": false,
  "record": {
    "abstract": "We propose a model of fractal point process driven by the nonlinear\nstochastic differential equation. The model is adjusted to the empirical data\nof trading activity in financial markets. This reproduces the probability\ndistribution function and power spectral density of trading activity observed\nin the stock markets. We present a simple stochastic relation between the\ntrading activity and return, which enables us to reproduce long-range memory\nstatistical properties of volatility by numerical calculations based on the\nproposed fractal point process.",
    "arxiv_id": "physics/0608036",
    "authors": [
      "V. Gontis",
      "B. Kaulakys"
    ],
    "categories": [
      "physics.soc-ph",
      "q-fin.ST"
    ],
    "doi": "10.1016/j.physa.2007.02.012",
    "title": "Modeling long-range memory trading activity by stochastic differential   equations",
    "url": "https://arxiv.org/abs/physics/0608036"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7abdffd2-21d9-455d-b399-4de1d653242f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}