{
  "id": "1110.1254",
  "version": "v3",
  "published": "2011-10-06T13:26:19.000Z",
  "updated": "2015-06-03T13:21:26.000Z",
  "title": "Random walks in cones",
  "authors": [
    "Denis Denisov",
    "Vitali Wachtel"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/13-AOP867 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2015, Vol. 43, No. 3, 992-1044",
  "doi": "10.1214/13-AOP867",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the asymptotic behavior of a multidimensional random walk in a general cone. We find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk conditioned to stay in a cone. The main step in the proof consists in constructing a positive harmonic function for our random walk under minimal moment restrictions on the increments. For the proof of tail asymptotics and integral limit theorems, we use a strong approximation of random walks by Brownian motion. For the proof of local limit theorems, we suggest a rather simple approach, which combines integral theorems for random walks in cones with classical local theorems for unrestricted random walks. We also discuss some possible applications of our results to ordered random walks and lattice path enumeration.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-08-15T15:21:32.000Z",
      "title": "Random Walks in Cones",
      "abstract": "We study the asymptotic behaviour of a multidimensional random walk in a general cone. We find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk conditioned to stay in a cone. The main step in the proof consists in constructing a positive harmonic function for our random walk under minimal moment restrictions on the increments. For the proof of all asymptotic relations we use the strong approximation of random walks by the Brownian motion.",
      "comment": "41 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-06-03T13:21:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50"
    ],
    "keywords": [
      "multidimensional random walk",
      "local limit theorems",
      "minimal moment restrictions",
      "proof consists",
      "general cone"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.1254D"
    }
  }
}