There is a large literature on boundary-crossing probabilities for random walks and Brownian motion,
starting from a seminal paper by Blackwell and Freedman (1964). We discuss some recent boundary-crossing probability
estimates for non Markovian, self-similar Gaussian processes. Those Gaussian processes include, in particular,
fractional Brownian motion. We use this connection to present an application in the study of points of slow growth for
certain types of parabolic stochastic PDEs. The latter is an attempt to describe the non-trivial nature of the onset of noise in such systems.