Gaussian Hilbert spaces / Svante Janson

This book studies extensively the various aspects of Gaussian Hilbert spaces (GHS) over the fields of real and complex numbers. The notion of Gaussian Hilbert spaces is an absolutely basic one with the most basic example being the linear span of a single normal random variable. The book offers a broad overview of the connections of GHS with problems in the theory of random processes and fields, stochastic calculus, quantum field theory, nonparametric statistics and partial differential equations. It should be fairly accessible to a graduate student who has taken some basic courses in functional analysis and probability theory. One of the nice aspects of this book is that it provides a common framework under which such diverse topics as the Malliavin calculus, nonparametric statistics, Feynman diagrams, random graphs, Fock space theory, etc., can be studied. (MathSciNet)

Bibliogr. p. 329-334. Index