{
  "id": "2210.01524",
  "version": "v1",
  "published": "2022-10-04T11:06:00.000Z",
  "updated": "2022-10-04T11:06:00.000Z",
  "title": "A new class of stochastic processes with great potential for interesting applications",
  "authors": [
    "Fulgence Eyi Obiang",
    "Paule Joyce Mbenangoya",
    "Magloire Yorick Nguema MBA",
    "Octave Moutsinga"
  ],
  "comment": "23 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper contributes to the study of a new and remarkable family of stochastic processes that we will term class $\\Sigma^{r}(H)$. This class is potentially interesting because it unifies the study of two known classes: the class $(\\Sigma)$ and the class $\\mathcal{M}(H)$. In other words, we consider the stochastic processes $X$ which decompose as $X=m+v+A$, where $m$ is a local martingale, $v$ and $A$ are finite variation processes such that $dA$ is carried by $\\{t\\geq0:X_{t}=0\\}$ and the support of $dv$ is $H$, the set of zeros of some continuous martingale $D$. First, we introduce a general framework. Thus, we provide some examples of elements of the new class and present some properties. Second, we provide a series of characterization results. Afterwards, we derive some representation results which permit to recover a process of the class $\\Sigma^{r}(H)$ from its final value and of the honest times $g=\\sup\\{t\\geq0:X_{t}=0\\}$ and $\\gamma=\\sup{H}$. In final, we investigate an interesting application with processes presently studied. More precisely, we construct solutions for skew Brownian motion equations using stochastic processes of the class $\\Sigma^{r}(H)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-04T11:06:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G07",
      "60G20",
      "60G46",
      "60G48"
    ],
    "keywords": [
      "stochastic processes",
      "interesting application",
      "great potential",
      "skew brownian motion equations",
      "finite variation processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}