{
  "id": "math/0410106",
  "version": "v1",
  "published": "2004-10-05T17:10:12.000Z",
  "updated": "2004-10-05T17:10:12.000Z",
  "title": "p-variation of strong Markov processes",
  "authors": [
    "Martynas Manstavicius"
  ],
  "comment": "Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/009117904000000423",
  "journal": "Annals of Probability 2004, Vol. 32, No. 3A, 2053-2066",
  "doi": "10.1214/009117904000000423",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let \\xi_t, t\\in[0,T], be a strong Markov process with values in a complete separable metric space (X,\\rho) and with transition probability function P_{s,t}(x,dy), 0\\le s\\le t\\le T, x\\in X. For any h\\in[0,T] and a>0, consider the function \\alpha(h,a)=sup\\bigl{P_{s,t}\\bigl(x,{y:\\rho(x,y)\\ge a}\\bigr):x\\in X,0\\le s\\le t\\le (s+h)\\wedge T\\bigr}. It is shown that a certain growth condition on \\alpha(h,a), as a\\downarrow0 and h stays fixed, implies the almost sure boundedness of the p-variation of \\xi_t, where p depends on the rate of growth.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-10-05T17:10:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25",
      "60G17",
      "60J35",
      "60G40"
    ],
    "keywords": [
      "strong markov processes",
      "p-variation",
      "complete separable metric space",
      "transition probability function",
      "growth condition"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10106M"
    }
  }
}