I'm looking at the problem of computing the simultaneous confidence bands for Gaussian processes. It can be stated at, given a Gaussian process X(t) with mean function \mu(t), covariance function k(t, t') and a coverage probability (1-\alpha), find c such that: Pr{ X(t) \in [\mu(t) - c\sqrt{\k(t, t)}, \mu(t) + c\sqrt{\k(t, t)} \forall t \in [a, b]} = \alpha.
I know that "Simultaneous confidence bands for random functions" (Knowles, 1988) gives the result for one-dimensional functions. But for high-dimensional functions, it only has asymptotic results for the case $t \rightarrow \infty$. My question is, Is there other result that is general and applies for all t in the high-dimensional case? Thanks!
