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For a centered Gaussian process $(X_t)_{t\in T}$ with canonical pseudometric $d(s,t)^2=\mathbb E|X_s-X_t|^2$,
$$
\mathbb E\sup_{t\in T}X_t
\leq C\int_0^{\operatorname{diam}(T)}
\sqrt{\log N(\epsilon,T,d)}\,d\epsilon,
$$
where $N(\epsilon,T,d)$ is the covering number.


Dudley entropy integral

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 210 / 4 / Solution

Dudley entropy integral

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Dudley entropy integral

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