J. Durbin, The First-Passage Density of a Continuous Gaussian Process to a General Boundary, Journal of Applied Probability, Vol. 22, No. 1 (Mar., 1985), pp. 99-122 ...

Gaussian processes, characterised by their fully specified means and covariances, offer a flexible non-parametric approach to surrogate modelling, statistical learning, and uncertainty quantification.

Since a Gaussian process defined on a compact parameter space that is a.s. continuous at each point is sample continuous, our result can be applied to the problem of general sample continuity of ...