{
  "id": "1607.03661",
  "version": "v1",
  "published": "2016-07-13T09:53:54.000Z",
  "updated": "2016-07-13T09:53:54.000Z",
  "title": "Asymptotic behavior of homogeneous additive functionals of the solutions of Itô stochastic differential equations with nonregular dependence on parameter",
  "authors": [
    "Grigorij Kulinich",
    "Svitlana Kushnirenko",
    "Yuliia Mishura"
  ],
  "comment": "Published at http://dx.doi.org/10.15559/16-VMSTA58 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/)",
  "journal": "Modern Stochastics: Theory and Applications 2016, Vol. 3, No. 2, 191-208",
  "doi": "10.15559/16-VMSTA58",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the asymptotic behavior of mixed functionals of the form $I_T(t)=F_T(\\xi_T(t))+\\int_0^tg_T(\\xi_T(s))\\,d\\xi_T(s)$, $t\\ge0$, as $T\\to\\infty$. Here $\\xi_T(t)$ is a strong solution of the stochastic differential equation $d\\xi_T(t)=a_T(\\xi_T(t))\\,dt+dW_T(t)$, $T>0$ is a parameter, $a_T=a_T(x)$ are measurable functions such that $\\left|a_T(x)\\right|\\leq C_T$ for all $x\\in \\mathbb {R}$, $W_T(t)$ are standard Wiener processes, $F_T=F_T(x)$, $x\\in \\mathbb {R}$, are continuous functions, $g_T=g_T(x)$, $x\\in \\mathbb {R}$, are locally bounded functions, and everything is real-valued. The explicit form of the limiting processes for $I_T(t)$ is established under very nonregular dependence of $g_T$ and $a_T$ on the parameter $T$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-13T09:53:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic differential equation",
      "homogeneous additive functionals",
      "nonregular dependence",
      "asymptotic behavior",
      "standard wiener processes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}