{
  "id": "2006.01887",
  "version": "v1",
  "published": "2020-06-02T19:11:32.000Z",
  "updated": "2020-06-02T19:11:32.000Z",
  "title": "Wiener-Hopf Factorization for Arithmetic Brownian Motion with Time-Dependent Drift and Volatility",
  "authors": [
    "Tomasz R. Bielecki",
    "Ziteng Cheng",
    "Ruoting Gong"
  ],
  "comment": "50 pages, 1 table",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we obtain a Wiener-Hopf type factorization for a time-inhomogeneous arithmetic Brownian motion with deterministic time-dependent drift and volatility. To the best of our knowledge, this paper is the very first step towards realizing the objective of deriving Wiener-Hopf type factorizations for (real-valued) time-inhomogeneous L\\'{e}vy processes. In particular, we argue that the classical Wiener-Hopf factorization for time-homogeneous L\\'{e}vy processes quite likely does not carry over to the case of time-inhomogeneous L\\'{e}vy processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-02T19:11:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "60J25",
      "60J65"
    ],
    "keywords": [
      "wiener-hopf factorization",
      "volatility",
      "deterministic time-dependent drift",
      "time-inhomogeneous arithmetic brownian motion",
      "deriving wiener-hopf type factorizations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}