{
  "id": "1105.0632",
  "version": "v2",
  "published": "2011-05-03T16:47:15.000Z",
  "updated": "2012-05-22T08:19:28.000Z",
  "title": "Regularity of affine processes on general state spaces",
  "authors": [
    "Martin Keller-Ressel",
    "Walter Schachermayer",
    "Josef Teichmann"
  ],
  "comment": "minor corrections",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a stochastically continuous, affine Markov process in the sense of Duffie, Filipovic and Schachermayer, with cadlag paths, on a general state space D, i.e. an arbitrary Borel subset of R^d. We show that such a process is always regular, meaning that its Fourier-Laplace transform is differentiable in time, with derivatives that are continuous in the transform variable. As a consequence, we show that generalized Riccati equations and Levy-Khintchine parameters for the process can be derived, as in the case of $D = R_+^m \\times R^n$ studied in Duffie, Filipovic and Schachermayer (2003). Moreover, we show that when the killing rate is zero, the affine process is a semi-martingale with absolutely continuous characteristics up to its time of explosion. Our results generalize the results of Keller-Ressel, Schachermayer and Teichmann (2011) for the state space $R_+^m \\times R^n$ and provide a new probabilistic approach to regularity.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-05-22T08:19:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25"
    ],
    "keywords": [
      "general state space",
      "affine processes",
      "regularity",
      "schachermayer",
      "affine markov process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.0632K"
    }
  }
}