Fleming's Randomized Game and His Parabolic Partial Differential Equation,
Abstract
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 1964 randomized 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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1974
- Accession Number
- AD0783698
Entities
People
- John M. Danskin
Organizations
- University of California, Berkeley