{
  "id": "1310.4722",
  "version": "v2",
  "published": "2013-10-17T14:40:08.000Z",
  "updated": "2013-10-23T10:25:51.000Z",
  "title": "Transformations of Wiener Measure and Orthogonal Expansions",
  "authors": [
    "Andrey A. Dorogovtsev",
    "Georgii V. Riabov"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we study the structure of square integrable functionals measurable with respect to coalescing stochastic flows. The case of $L^2$ space generated by the process $\\eta(\\cdot)=w(\\min(\\tau,\\cdot)),$ where $w$ is a Brownian motion and $\\tau$ is the first moment when $w$ hits the given continuous function $g$ is considered. We present a new construction of multiple stochastic integrals with respect to the process $\\eta.$ Our approach is based on the change of measure technique. The analogue of the It\\^o-Wiener expansion for the space $L^2(\\eta)$ is constructed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-10-23T10:25:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "wiener measure",
      "orthogonal expansions",
      "transformations",
      "multiple stochastic integrals",
      "coalescing stochastic flows"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.4722D"
    }
  }
}