Gaussian Random Functions

This text presents a mathematically complete series of the most essential properties of Gaussian random functions. It focuses on a number of fundamental objects in the theory of Gaussian random functions and exposes their interrelations. The basic plots presented in the book embody: the kernel of a Gaussian measure; the model of a Gaussian random function; oscillations of sample functions; the convexity and isoperimetric inequalities; the regularity of sample functions of means of entropy characteristics and the majorizing measures; functional laws of the iterated logarithm and estimates for the probabilities of large deviations. This book should be of interest to mathematicians and scientists who use stochastic methods in their research and to students in probability theory.