{
  "id": "2010.02465",
  "version": "v1",
  "published": "2020-10-06T04:12:16.000Z",
  "updated": "2020-10-06T04:12:16.000Z",
  "title": "A study of backward stochastic differential equation on a Riemannian manifold",
  "authors": [
    "Xin Chen",
    "Wenjie Ye"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Suppose $N$ is a compact Riemannian manifold, in this paper we will introduce the definition of $N$-valued BSDE and $L^2(\\mathbb{T}^m;N)$-valued BSDE for which the solution are not necessarily staying in only one local coordinate. Moreover, the global existence of a solution to $L^2(\\mathbb{T}^m;N)$-valued BSDE will be proved without any convexity condition on $N$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-06T04:12:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "backward stochastic differential equation",
      "valued bsde",
      "compact riemannian manifold",
      "local coordinate",
      "convexity condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}