{
  "id": "2310.06416",
  "version": "v1",
  "published": "2023-10-10T08:37:25.000Z",
  "updated": "2023-10-10T08:37:25.000Z",
  "title": "Stochastic representation of processes with resetting",
  "authors": [
    "Marcin Magdziarz",
    "Kacper Taźbierski"
  ],
  "journal": "Phys. Rev. E 106, 014147 (2022)",
  "doi": "10.1103/PhysRevE.106.014147",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we introduce a general stochastic representation for an important class of processes with resetting. It allows to describe any stochastic process intermittently terminated and restarted from a predefined random or non-random point. Our approach is based on stochastic differential equations called jump-diffusion models. It allows to analyze processes with resetting both, analytically and using Monte Carlo simulation methods. To depict the strength of our approach, we derive a number of fundamental properties of Brownian motion with Poissonian resetting, such as: the It\\^o lemma, the moment-generating function, the characteristic function, the explicit form of the probability density function, moments of all orders, various forms of the Fokker-Planck equation, infinitesimal generator of the process and its adjoint operator. Additionally, we extend the above results to the case of time-nonhomogeneous Poissonian resetting. This way we build a general framework for the analysis of any stochastic process with intermittent random resetting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-10T08:37:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J75",
      "G.3"
    ],
    "keywords": [
      "stochastic process",
      "monte carlo simulation methods",
      "general stochastic representation",
      "probability density function",
      "stochastic differential equations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}