{
  "id": "0801.3505",
  "version": "v1",
  "published": "2008-01-23T06:04:58.000Z",
  "updated": "2008-01-23T06:04:58.000Z",
  "title": "Harmonic Analysis of Stochastic Equations and Backward Stochastic Differential Equations",
  "authors": [
    "Freddy Delbaen",
    "Shanjian Tang"
  ],
  "comment": "40 pages",
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "The BMO martingale theory is extensively used to study nonlinear multi-dimensional stochastic equations (SEs) in $\\cR^p$ ($p\\in [1, \\infty)$) and backward stochastic differential equations (BSDEs) in $\\cR^p\\times \\cH^p$ ($p\\in (1, \\infty)$) and in $\\cR^\\infty\\times \\bar{\\cH^\\infty}^{BMO}$, with the coefficients being allowed to be unbounded. In particular, the probabilistic version of Fefferman's inequality plays a crucial role in the development of our theory, which seems to be new. Several new results are consequently obtained. The particular multi-dimensional linear case for SDEs and BSDEs are separately investigated, and the existence and uniqueness of a solution is connected to the property that the elementary solutions-matrix for the associated homogeneous SDE satisfies the reverse H\\\"older inequality for some suitable exponent $p\\ge 1$. Finally, we establish some relations between Kazamaki's quadratic critical exponent $b(M)$ of a BMO martingale $M$ and the spectral radius of the solution operator for the $M$-driven SDE, which lead to a characterization of Kazamaki's quadratic critical exponent of BMO martingales being infinite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-01-23T06:04:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60H20",
      "60H99",
      "60G44",
      "60G46"
    ],
    "keywords": [
      "backward stochastic differential equations",
      "harmonic analysis",
      "kazamakis quadratic critical exponent",
      "bmo martingale",
      "study nonlinear multi-dimensional stochastic equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}