{
  "id": "1406.4759",
  "version": "v1",
  "published": "2014-06-18T15:10:36.000Z",
  "updated": "2014-06-18T15:10:36.000Z",
  "title": "Harnack Inequalities for Degenerate Diffusions",
  "authors": [
    "Charles L. Epstein",
    "Camelia A. Pop"
  ],
  "comment": "57 pages",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We study various probabilistic and analytical properties of a class of degenerate diffusion operators arising in Population Genetics, the so-called generalized Kimura diffusion operators. Our main results is a stochastic representation of weak solutions to a degenerate parabolic equation with singular lower-order coefficients, and the proof of the scale-invariant Harnack inequality for nonnegative solutions to the Kimura parabolic equation. The stochastic representation of solutions that we establish is a considerable generalization of the classical results on Feynman-Kac formulas concerning the assumptions on the degeneracy of the diffusion matrix, the boundedness of the drift coefficients, and on the a priori regularity of the weak solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-18T15:10:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic representation",
      "weak solutions",
      "singular lower-order coefficients",
      "scale-invariant harnack inequality",
      "degenerate parabolic equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.4759E"
    }
  }
}