{
  "id": "1205.2413",
  "version": "v2",
  "published": "2012-05-11T01:47:42.000Z",
  "updated": "2013-05-26T15:17:26.000Z",
  "title": "Diffusions of Multiplicative Cascades",
  "authors": [
    "Tom Alberts",
    "Ben Rifkind"
  ],
  "comment": "30 pages; added section on Holder continuity",
  "categories": [
    "math.PR"
  ],
  "abstract": "A multiplicative cascade can be thought of as a randomization of a measure on the boundary of a tree, constructed from an iid collection of random variables attached to the tree vertices. Given an initial measure with certain regularity properties, we construct a continuous time, measure-valued process whose value at each time is a cascade of the initial one. We do this by replacing the random variables on the vertices with independent increment processes satisfying certain moment assumptions. Our process has a Markov property: at any given time it is a cascade of the process at any earlier time by random variables that are independent of the past. It has the further advantage of being a martingale and, under certain extra conditions, it is also continuous. We discuss applications of this process to models of tree polymers and one-dimensional random geometry.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-26T15:17:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiplicative cascade",
      "random variables",
      "diffusions",
      "one-dimensional random geometry",
      "independent increment processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.2413A"
    }
  }
}