{
  "id": "2012.11200",
  "version": "v1",
  "published": "2020-12-21T09:30:00.000Z",
  "updated": "2020-12-21T09:30:00.000Z",
  "title": "Martingale Decomposition and BSDE on Time Scales",
  "authors": [
    "Guofeng Tang"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we present martingale decomposition on time scales. We establish the related backward stochastic dynamic equations on time scales (this paper BS$\\nabla$E for short, concerning $\\nabla$-integral on time scales) which unify backward stochastic differential equations and backward stochastic difference equations. We prove the existence and uniqueness theorem of BS$\\nabla$E. This work can be considered as a unification and a generalization of similar results in backward stochastic difference equations and backward stochastic differential equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-21T09:30:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "time scales",
      "backward stochastic differential equations",
      "martingale decomposition",
      "backward stochastic difference equations",
      "backward stochastic dynamic equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}