{
  "annotation_id": "58925fa0-4095-48ac-a3ff-b114f971b0e8",
  "date_created": "2026-03-02T18:01:24.900000Z",
  "date_modified": "2026-03-02T18:01:24.900000Z",
  "file_hash": "17adbae198b6ab30253473d78ef87405af148565c5ac7c2dc72f970ca0ee0539",
  "private": false,
  "record": {
    "abstract": "A stochastic leap-frog algorithm for the numerical integration of Brownian\nmotion stochastic differential equations with multiplicative noise is proposed\nand tested. The algorithm has a second-order convergence of moments in a finite\ntime interval and requires the sampling of only one uniformly distributed\nrandom variable per time step. The noise may be white or colored. We apply the\nalgorithm to a study of the approach towards equilibrium of an oscillator\ncoupled nonlinearly to a heat bath and investigate the effect of the\nmultiplicative noise (arising from the nonlinear coupling) on the relaxation\ntime. This allows us to test the regime of validity of the energy-envelope\napproximation method.",
    "arxiv_id": "physics/9912055",
    "authors": [
      "Ji Qiang",
      "Salman Habib"
    ],
    "categories": [
      "physics.comp-ph"
    ],
    "doi": "10.1103/PhysRevE.62.7430",
    "title": "A Second-Order Stochastic Leap-Frog Algorithm for Multiplicative Noise   Brownian Motion",
    "url": "https://arxiv.org/abs/physics/9912055"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "365e4186-3d9e-414d-a4ef-fc094b965dfe",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}