{
  "id": "1711.01168",
  "version": "v1",
  "published": "2017-11-02T06:23:17.000Z",
  "updated": "2017-11-02T06:23:17.000Z",
  "title": "Asymptotic behavior of functionals of the solutions to inhomogeneous Itô stochastic differential equations with nonregular dependence on parameter",
  "authors": [
    "Grigorij Kulinich",
    "Svitlana Kushnirenko"
  ],
  "comment": "Published at http://dx.doi.org/10.15559/17-VMSTA83 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/). arXiv admin note: text overlap with arXiv:1607.03661",
  "journal": "Modern Stochastics: Theory and Applications 2017, Vol. 4, No. 3, 199-217",
  "doi": "10.15559/17-VMSTA83",
  "categories": [
    "math.PR"
  ],
  "abstract": "The asymptotic behavior, as $T\\to\\infty$, of some functionals of the form $I_T(t)=F_T(\\xi_T(t))+\\int_0^tg_T(\\xi_T(s))\\,dW_T(s)$, $t\\ge0$ is studied. Here $\\xi_T(t)$ is the solution to the time-inhomogeneous It\\^{o} stochastic differential equation \\[d\\xi_T(t)=a_T\\bigl(t,\\xi_T(t)\\bigr)\\,dt+dW_T(t),\\quad t\\ge0, \\xi_T(0)=x_0,\\] $T>0$ is a parameter, $a_T(t,x),x\\in\\mathbb{R}$ are measurable functions, $|a_T(t,x)|\\leq C_T$ for all $x\\in\\mathbb{R}$ and $t\\ge0$, $W_T(t)$ are standard Wiener processes, $F_T(x),x\\in\\mathbb{R}$ are continuous functions, $g_T(x),x\\in\\mathbb{R}$ are measurable locally bounded functions, and everything is real-valued. The explicit form of the limiting processes for $I_T(t)$ is established under nonregular dependence of $a_T(t,x)$ and $g_T(x)$ on the parameter $T$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-02T06:23:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic differential equation",
      "asymptotic behavior",
      "nonregular dependence",
      "functionals",
      "standard wiener processes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}