{
  "id": "0707.4536",
  "version": "v1",
  "published": "2007-07-31T05:39:04.000Z",
  "updated": "2007-07-31T05:39:04.000Z",
  "title": "On the paper ``Weak convergence of some classes of martingales with jumps''",
  "authors": [
    "Yoichi Nishiyama"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/009117906000000755 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2007, Vol. 35, No. 3, 1194-1200",
  "doi": "10.1214/009117906000000755",
  "categories": [
    "math.PR"
  ],
  "abstract": "This note extends some results of Nishiyama [Ann. Probab. 28 (2000) 685--712]. A maximal inequality for stochastic integrals with respect to integer-valued random measures which may have infinitely many jumps on compact time intervals is given. By using it, a tightness criterion is obtained; if the so-called quadratic modulus is bounded in probability and if a certain entropy condition on the parameter space is satisfied, then the tightness follows. Our approach is based on the entropy techniques developed in the modern theory of empirical processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-31T05:39:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60F17"
    ],
    "keywords": [
      "weak convergence",
      "martingales",
      "compact time intervals",
      "integer-valued random measures",
      "note extends"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.4536N"
    }
  }
}