{
  "id": "1202.4006",
  "version": "v1",
  "published": "2012-02-17T20:23:12.000Z",
  "updated": "2012-02-17T20:23:12.000Z",
  "title": "Maximum principle for optimal control of stochastic partial differential equations",
  "authors": [
    "AbdulRahman Al-Hussein"
  ],
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "We shall consider a stochastic maximum principle of optimal control for a control problem associated with a stochastic partial differential equations of the following type: d x(t) = (A(t) x(t) + a (t, u(t)) x(t) + b(t, u(t)) dt + [<\\sigma(t, u(t)), x(t)>_K + g (t, u(t))] dM(t), x(0) = x_0 \\in K, with some given predictable mappings $a, b, \\sigma, g$ and a continuous martingale $M$ taking its values in a Hilbert space $K,$ while $u(\\cdot)$ represents a control. The equation is also driven by a random unbounded linear operator $A(t,w), \\; t \\in [0,T ], $ on $K .$ We shall derive necessary conditions of optimality for this control problem without a convexity assumption on the control domain, where $u(\\cdot)$ lives, and also when this control variable is allowed to enter in the martingale part of the equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-02-17T20:23:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic partial differential equations",
      "optimal control",
      "control problem",
      "stochastic maximum principle",
      "random unbounded linear operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.4006A"
    }
  }
}