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I am trying to obtain an explicit expression for $C$ in terms of $b$ in the following inequality. Suppose that $Y$ is a centred Gaussian random vector in $\mathbb R^p$ such that $\operatorname EY_j^...

Let $E$ be a separable Banach space, consider a centered $E$-valued Gaussian process $\{x_t,t\ge 0\}$ that satisfies \begin{equation} \mathbb{E}\phi(x_s)\psi(x_t)=R(s,t)K(\phi,\psi),\quad \phi,\psi\in ...

Let $X_t, t \in T$ denote a centered Gaussian process. Let $d(t, s) = \sqrt{\mathbb{E} (X_t - X_s)^2}$. Consider a mean function $t \mapsto \mu_t$. Define the expected supremum $$ S(T, \mu) = \mathbb{...