{
  "id": "2005.04030",
  "version": "v1",
  "published": "2020-05-08T13:26:23.000Z",
  "updated": "2020-05-08T13:26:23.000Z",
  "title": "An ideal class to construct solutions for skew Brownian motion equations",
  "authors": [
    "Fulgence Eyi Obiang",
    "Octave Moutsinga",
    "Youssef Ouknine"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "The present work focuses on the study of the $(\\Sigma)$ class and consists of two main parts. In the first one, we extend the notion of semi-martingales of class $(\\Sigma)$ to c\\`adl\\`ag semi-martingales whose the finite variational part is considered c\\`adl\\`ag instead of continuous. So, we propose a general framework dealing with such processes by extending some known results of the previous versions of the class $(\\Sigma)$. The second part is dedicated to the study of continuous processes of the class $(\\Sigma)$. More precisely, we first derive a series of new characterization results for such processes. Afterwards, we construct solutions for the skew Brownian motion equations using stochastic processes of the class $(\\Sigma)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-08T13:26:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G07",
      "60G20",
      "60G46",
      "60G48"
    ],
    "keywords": [
      "skew brownian motion equations",
      "construct solutions",
      "ideal class",
      "finite variational part",
      "stochastic processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}