  Let $\{X(t), t\geq0\}$ be a stationary Gaussian process with zero-mean and
unit variance. A deep result derived in Piterbarg (2004), which we refer to as
Piterbarg's max-discretisation theorem gives the joint asymptotic behaviour
($T\to \infty$) of the continuous time maximum $M(T)=\max_{t\in [0,T]} X(t), $
and the maximum $M^{\delta}(T)=\max_{t\in \mathfrak{R}(\delta)}X(t), $ with
$\mathfrak{R}(\delta) \subset [0,T]$ a uniform grid of points of distance
$\delta=\delta(T)$. Under some asymptotic restrictions on the correlation
function Piterbarg's max-discretisation theorem shows that for the limit result
it is important to know the speed $\delta(T)$ approaches 0 as $T\to \infty$.
The present contribution derives the aforementioned theorem for multivariate
stationary Gaussian processes.
