{
  "id": "1510.07166",
  "version": "v1",
  "published": "2015-10-24T17:10:02.000Z",
  "updated": "2015-10-24T17:10:02.000Z",
  "title": "Path integral representation for stochastic jump processes with boundaries",
  "authors": [
    "Takashi Arai"
  ],
  "comment": "16 pages",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We propose a formalism to analyze discrete stochastic processes with finite-state-level N. By using an (N+1)-dimensional representation of su(2) Lie algebra, we re-express the master equation to a time-evolution equation for the state vector corresponding to the probability generating function. We found that the generating function of the system can be expressed as a propagator in the spin coherent state representation. The generating function has a path integral representation in terms of the spin coherent state. We apply our formalism to a linear Susceptible-Infected-Susceptible (SIS) epidemic model with time-dependent transition probabilities. The probability generating function of the system is calculated concisely using an algebraic property of the system or a path integral representation. Our results indicate that the method of analysis developed in the field of quantum mechanics is applicable to discrete stochastic processes with finite-state-level.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-24T17:10:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "path integral representation",
      "stochastic jump processes",
      "probability generating function",
      "spin coherent state representation",
      "analyze discrete stochastic processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151007166A"
    }
  }
}