{
  "id": "1207.2281",
  "version": "v1",
  "published": "2012-07-10T09:42:07.000Z",
  "updated": "2012-07-10T09:42:07.000Z",
  "title": "New classes of processes in stochastic calculus for signed measures",
  "authors": [
    "Fulgence Eyi Obiang",
    "Youssef Ouknine",
    "Octave Moutsinga"
  ],
  "comment": "23 pages. arXiv admin note: text overlap with arXiv:math/0505515",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let us consider a signed measure $\\Qv$ and a probability measure $\\Pv$ such that $\\Qv<<\\Pv$. Let $D$ be the density of $\\Qv$ with respect to $\\Pv$. $H$ represents the set of zeros of $D$, $\\bar{g}=0\\vee\\sup{H}$. In this paper, we shall consider two classes of nonnegative processes of the form $X_{t}=N_{t}+A_{t}$. The first one is the class of semimartingales where $ND$ is a cadlag local martingale and $A$ is a continuous and non-decreasing process such that $(dA_{t})$ is carried by $H\\cup\\{t: X_{t}=0\\}$. The second one is the case where $N$ and $A$ are null on $H$ and $A_{.+\\bar{g}}$ is a non-decreasing, continuous process such that $(dA_{t+\\bar{g}})$ is carried by $\\{t: X_{t+\\bar{g}}=0\\}$. We shall show that these classes are extensions of the class $(\\sum)$ defined by A.Nikeghbali \\cite{nik} in the framework of stochastic calculus for signed measures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-10T09:42:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "signed measure",
      "stochastic calculus",
      "cadlag local martingale",
      "probability measure",
      "nonnegative processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.2281E"
    }
  }
}