{
  "id": "1112.2332",
  "version": "v2",
  "published": "2011-12-11T07:47:56.000Z",
  "updated": "2012-11-12T15:07:11.000Z",
  "title": "Mixed stochastic differential equations with long-range dependence: existence, uniqueness and convergence of solutions",
  "authors": [
    "Yuliya Mishura",
    "Georgiy Shevchenko"
  ],
  "journal": "Comput. Math. Appl. 64 (2012), 3217-3227",
  "doi": "10.1016/j.camwa.2012.03.061",
  "categories": [
    "math.PR"
  ],
  "abstract": "For a mixed stochastic differential equation involving standard Brownian motion and an almost surely H\\\"older continuous process $Z$ with H\\\"older exponent $\\gamma>1/2$, we establish a new result on its unique solvability. We also establish an estimate for difference of solutions to such equations with different processes $Z$ and deduce a corresponding limit theorem. As a by-product, we obtain a result on existence of moments of a solution to a mixed equation under an assumption that $Z$ has certain exponential moments.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-12T15:07:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G22",
      "60G15",
      "60H10",
      "26A33"
    ],
    "keywords": [
      "mixed stochastic differential equation",
      "long-range dependence",
      "convergence",
      "uniqueness",
      "standard brownian motion"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.2332M"
    }
  }
}