{
  "id": "1402.0748",
  "version": "v1",
  "published": "2014-02-04T14:41:28.000Z",
  "updated": "2014-02-04T14:41:28.000Z",
  "title": "Deterministic and Stochastic Differential Equations in Hilbert Spaces Involving Multivalued Maximal Monotone Operators",
  "authors": [
    "Aurel Rascanu"
  ],
  "comment": "This is an electronic reprint of the original article published by the Panamer. Math. J. 6 (1996), no. 3, 83--119, MR1400370. This reprint differs from the original in pagination and typographic detail. The article is posted on ArXiv.org because the online version is not available on the web page of the PanAmerican Mathematical Journal",
  "journal": "Panamer. Math. J. 6 (1996), no. 3, 83--119, MR1400370",
  "categories": [
    "math.DS",
    "math.PR"
  ],
  "abstract": "This work deals with a Skorokhod problem driven by a maximal operator: \\begin{aligned} &du(t)+Au(t)(dt)\\ni f(t)dt+dM(t), \\; 0<t<T,\\\\ &u(0)=u_{0}, \\end{aligned} which is a multivalued deterministic differential equation with a singular inputs $dM(t)$, where $t\\rightarrow M(t)$ is a continuous function. The existence and uniqueness result is used to study an It\\^{o}'s stochastic differential equation \\begin{aligned} &du(t)+Au(t)(dt)\\ni f(t,u(t))dt+B(t,u(t))dW(t),\\; 0<t<T,\\\\ &u(0)=u_{0}, \\end{aligned} in a real Hilbert space $H$, where $A$ is a multivalued ($\\alpha$-)maximal monotone operator on $H$, and $f(t,u)$ and $B(t,u)$ are Lipschitz continuous with respect to $u$. Some asymptotic properties in the stochastic case are also found.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-04T14:41:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60H15",
      "47N20",
      "47N30"
    ],
    "keywords": [
      "stochastic differential equation",
      "multivalued maximal monotone operators",
      "skorokhod problem driven",
      "real hilbert space",
      "multivalued deterministic differential equation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.0748R"
    }
  }
}