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2022

Bounding suprema of canonical processes via convex hull

Latała, Rafał

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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.

Bounding suprema of canonical processes via convex hull · Around

Built on

C. A. Rogers, G. C. Shephard, Convex bodies associated with a given convex body
1958
Earlier work this paper cites.
H. P. Rosenthal On the subspaces of L p L^{p} ( p > 2 ) (p>2) spanned by sequences of independent random variables
1970
Earlier work this paper cites.
X. Fernique, Regularité des trajectoires des fonctions aléatoires gaussiennes
1975
Earlier work this paper cites.
M. Talagrand, Regularity of Gaussian processes
1987
Earlier work this paper cites.

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