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Fleming's Randomized Game and His Parabolic Partial Differential Equation,

机译:弗莱明的随机游戏和他的抛物型偏微分方程,

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Proceeding from first principles and making no use of existing partial differential equations (PDE) theory,the paper gives a direct and elementary proof that the value of Wendell Fleming's 1964randomized mixed-strategy game exists and satisfies his parabolic PDE. Fleming required the terminal function to have Lipschitzian first and second partial derivatives;this paper requires only that the terminal function and its gradient be Lipschitzian. The solution is given a new representation,which allows precise Lipschitz and Holder estimates to be made. A trick of Fleming allows the deduction of a uniqueness and existence theorem for a class of parabolic equations with Laplacian operator under the lightened terminal conditions. (Author)

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