Optimal Recovery Games on B
Houman Owhadi, Clint Scovel · Cambridge University Press eBooks · 2019
This chapter introduces optimal recovery games on Banach spaces, presents their natural lift to mixed strategies, and then characterizes their saddle points in terms of Gaussian measures, cylinder measures, and fields. The canonical Gaussian field is shown to be a universal field in the sense that its conditioning with respect to linear measurements produces optimal strategies. When those measurements form a nested hierarchy, hierarchies of optimal approximations form a martingale obtained by conditioning the Gaussian field on the filtration formed by those measurements.