{
  "id": "1007.2226",
  "version": "v2",
  "published": "2010-07-13T23:08:26.000Z",
  "updated": "2016-07-01T13:19:16.000Z",
  "title": "$L^p$ Solutions of Backward Stochastic Differential Equations with Jumps",
  "authors": [
    "Song Yao"
  ],
  "comment": "Keywords: Backward stochastic differential equations with jumps, $L^p$ solutions, monotonic generators, convolution with mollifiers",
  "categories": [
    "math.PR"
  ],
  "abstract": "Given $p \\in (1, 2)$, we study $L^p$-solutions of a multi-dimensional backward stochastic differential equation with jumps (BSDEJ) whose generator may not be Lipschitz continuous in $(y,z,u)$. We show that such a BSDEJ with a p-integrable terminal data admits a unique $L^p$ solution by approximating the monotonic generator by a sequence of Lipschitz generators via convolution with mollifiers and using a stability result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-13T23:08:26.000Z",
      "title": "Lp Solutions of Backward Stochastic Differential Equations with Jumps",
      "abstract": "In this paper, we study a multi-dimensional backward stochastic differential equation with Poisson jumps (BSDEJ) that has non-Lipschitz generator and infinity time horizon. For any $p \\in (1, \\infty)$, we show that the BSDEJ with a $p$-integrable terminal condition admits a unique solution of $L^p$-type.",
      "comment": "Keywords: Backward stochastic differential equation with jumps, $L^p$ solution, non-Lipschitz generator",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-07-01T13:19:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60G40",
      "60G55"
    ],
    "keywords": [
      "lp solutions",
      "multi-dimensional backward stochastic differential equation",
      "infinity time horizon",
      "integrable terminal condition admits",
      "poisson jumps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.2226Y"
    }
  }
}