Borell-TIS inequality
= Borell-TIS inequality
{c}
If a centered separable Gaussian process has finite expected supremum $m$ and $\sigma^2=\sup_t\operatorname{Var}(X_t)$, then
$$
\mathbb P\left(\sup_tX_t>m+u\right)
\leq e^{-u^2/(2\sigma^2)}.
$$
= Borell-TIS inequality
{c}
If a centered separable Gaussian process has finite expected supremum $m$ and $\sigma^2=\sup_t\operatorname{Var}(X_t)$, then
$$
\mathbb P\left(\sup_tX_t>m+u\right)
\leq e^{-u^2/(2\sigma^2)}.
$$