{
  "id": "0801.0330",
  "version": "v1",
  "published": "2008-01-02T02:39:17.000Z",
  "updated": "2008-01-02T02:39:17.000Z",
  "title": "Properties of Expectations of Functions of Martingale Diffusions",
  "authors": [
    "George Lowther"
  ],
  "comment": "24 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Given a real valued and time-inhomogeneous martingale diffusion X, we investigate the properties of functions defined by the conditional expectation f(t,X_t)=E[g(X_T)|F_t]. We show that whenever g is monotonic or Lipschitz continuous then f(t,x) will also be monotonic or Lipschitz continuous in x. If g is convex then f(t,x) will be convex in x and decreasing in t. We also define the marginal support of a process and show that it almost surely contains the paths of the process. Although f need not be jointly continuous, we show that it will be continuous on the marginal support of X. We prove these results for a generalization of diffusion processes that we call `almost-continuous diffusions', and includes all continuous and strong Markov processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-01-02T02:39:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "60J25",
      "60G44"
    ],
    "keywords": [
      "properties",
      "marginal support",
      "strong markov processes",
      "conditional expectation",
      "time-inhomogeneous martingale diffusion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.0330L"
    }
  }
}