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1 results

  • 8 - Optimal Recovery Games on Hs0(Ω)

  • from Part II - The Game Theoretic Approach
  • Houman Owhadi, California Institute of Technology, Clint Scovel, California Institute of Technology
  • Book:
    Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
    Published online:
    10 October 2019
    Print publication:
    24 October 2019, pp 119-130

  • Summary

    This chapter introduces two-person zero-sum games, optimal recovery games, and their lifts tomixed extended games and defines saddle points and minmax solutions.The optimal mixed strategy for the mixed extension of the optimal recovery games is generated by conditioning the canonical Gaussian field associated with the energy norm. Since the dependence ofthese optimal solutions on the measurement functions is through the conditioning process only, the canonical Gaussian field is referred to as a universal field. This fact demonstrates that the optimal solutions generated from a nested hierarchy of measurement functions form a martingale.