{
  "id": "1906.02081",
  "version": "v1",
  "published": "2019-06-05T15:42:55.000Z",
  "updated": "2019-06-05T15:42:55.000Z",
  "title": "Exact enumeration approach to first-passage time distribution of non-Markov random walks",
  "authors": [
    "Shant Baghram",
    "Farnik Nikakhtar",
    "M. Reza Rahimi Tabar",
    "Sohrab Rahvar",
    "Ravi K. Sheth",
    "Klaus Lehnertz",
    "Muhammad Sahimi"
  ],
  "comment": "23 pages, 4 figures, 1 table and 5 appendices. Published version",
  "journal": "Physical Review E 99, 062101 (2019)",
  "doi": "10.1103/PhysRevE.99.062101",
  "categories": [
    "cond-mat.stat-mech",
    "physics.data-an"
  ],
  "abstract": "We propose an analytical approach to study non-Markov random walks by employing an exact enumeration method. Using the method, we derive an exact expansion for the first-passage time (FPT) distribution for any continuous, differentiable non-Markov random walk with Gaussian or non-Gaussian multivariate distribution. As an example, we study the FPT distribution of a fractional Brownian motion with a Hurst exponent $H\\in(1/2,1)$ that describes numerous non-Markov stochastic phenomena in physics, biology and geology, and for which the limit $H=1/2$ represents a Markov process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-05T15:42:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first-passage time distribution",
      "exact enumeration approach",
      "study non-markov random walks",
      "differentiable non-markov random walk",
      "exact enumeration method"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}