Bounding suprema of canonical processes via convex hull
arXiv:2204.09463 · doi:10.1007/978-3-031-26979-0_13
Abstract
We discuss the method of bounding suprema of canonical processes based on the inclusion of their index set into a convex hull of a well-controlled set of points. While the upper bound is immediate, the reverse estimate was established to date only for a narrow class of regular stochastic processes. We show that for specific index sets, including arbitrary ellipsoids, regularity assumptions may be substantially weakened.
18 pages