{
  "id": "1512.06236",
  "version": "v1",
  "published": "2015-12-19T12:31:39.000Z",
  "updated": "2015-12-19T12:31:39.000Z",
  "title": "Weak Dirichlet processes with jumps",
  "authors": [
    "Elena Bandini",
    "Francesco Russo"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper develops systematically stochastic calculus via regularization in the case of jump processes. In particular one continues the analysis of real-valued c\\`adl\\`ag weak Dirichlet processes with respect to a given filtration. Such a process is the sum of a local martingale and an adapted process A such that $[N, A] = 0$, for any continuous local martingale $N$. In particular, given a function $u : [0, T ] \\times \\mathbb{R} \\rightarrow \\mathbb{R}$, which is of class C^{0,1} (or sometimes less), we provide a chain rule type expansion for X\\_t = u(t, X\\_t) which stands in applications for a chain It\\^o type rule.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-19T12:31:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weak dirichlet processes",
      "chain rule type expansion",
      "jump processes",
      "systematically stochastic calculus",
      "continuous local martingale"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151206236B"
    }
  }
}