Maximum of a Gaussian Process
Simeon M. Berman · 2017
This chapter provides the technical tools in the theory of Gaussian processes that are needed for the preliminary estimates of the extreme local fluctuations of the sample functions. These results are valid for general, not necessarily stationary, Gaussian processes. This material includes early results of X. Fernique and Simeon M. Berman. The latter results have been surpassed in generality in years, but are employed in their given forms because they are most easily applicable to the processes under consideration. The method that was used throughout the period was based on the approximation of the maximum of the continuous sample function by the maximum of a discrete skeleton obtained by sampling over an increasingly dense lattice on the real line.