{
  "id": "2211.15017",
  "version": "v1",
  "published": "2022-11-28T02:59:25.000Z",
  "updated": "2022-11-28T02:59:25.000Z",
  "title": "Random walks in time-inhomogeneous random environment conditioned to stay positive",
  "authors": [
    "Wenming Hong",
    "Shengli Liang"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a random walk $\\{S_n\\}_{n\\in \\mathbb{N}}$ in time-inhomogeneous random environment $\\xi$. For almost each realization of $\\xi$, we formulate a quenched harmonic function, based on which we can define the random walk in random environment conditioned to stay positive by the Doob's $h$-transform. Furthermore, we prove a quenched invariance principle for the conditioned random walk for almost each realization of $\\xi$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-28T02:59:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60K37",
      "60F17"
    ],
    "keywords": [
      "time-inhomogeneous random environment",
      "stay positive",
      "realization",
      "quenched invariance principle",
      "conditioned random walk"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}