{
  "id": "2109.03649",
  "version": "v1",
  "published": "2021-09-08T13:51:04.000Z",
  "updated": "2021-09-08T13:51:04.000Z",
  "title": "Field theory of survival probabilities, extreme values, first passage times, and mean span of non-Markovian stochastic processes",
  "authors": [
    "Benjamin Walter",
    "Gunnar Pruessner",
    "Guillaume Salbreux"
  ],
  "comment": "21 pages, 2 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We provide a perturbative framework to calculate extreme events of non-Markovian processes, by mapping the stochastic process to a two-species reaction diffusion process in a Doi-Peliti field theory combined with the Martin-Siggia-Rose formalism. This field theory treats interactions and the effect of external, possibly self-correlated noise in a perturbation about a Markovian process, thereby providing a systematic, diagrammatic approach to extreme events. We apply the formalism to Brownian Motion and calculate its survival probability distribution subject to self-correlated noise.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-08T13:51:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "field theory",
      "first passage times",
      "non-markovian stochastic processes",
      "mean span",
      "extreme values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}