{
  "id": "2001.09080",
  "version": "v1",
  "published": "2020-01-24T16:39:43.000Z",
  "updated": "2020-01-24T16:39:43.000Z",
  "title": "Cylindrical martingale-valued measures, stochastic integration and stochastic PDEs in Hilbert space",
  "authors": [
    "A. E. Alvarado-Solano",
    "C. A. Fonseca-Mora"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We introduce a theory of stochastic integration for operator-valued integrands with respect to some classes of cylindrical martingale-valued measures in Hilbert spaces. The integral is constructed using a novel technique that utilizes the radonification of cylindrical martingales by a Hilbert-Schmidt operator theorem. We apply the developed theory of stochastic integration to establish existence and uniqueness of weak and mild solutions for stochastic evolution equations driven by multiplicative cylindrical martingale-valued measure noise with rather general coefficients. Our theory covers the study of integration and of SPDEs driven by Hilbert space valued L\\'{e}vy noise (which is not required to satisfy any moment condition), cylindrical L\\'{e}vy noise with (weak) second moments and L\\'{e}vy-valued random martingale measures with finite second moment.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-24T16:39:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H05",
      "60H15",
      "60B11",
      "60G20"
    ],
    "keywords": [
      "stochastic integration",
      "hilbert space",
      "stochastic pdes",
      "cylindrical martingale-valued measure noise",
      "stochastic evolution equations driven"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}