Gaussian Measures in Hilbert Space

This book deals with the problems related to Gaussian measures in Hilbert and Banach spaces and lying on junction of Probability Theory and Functional Analysis. A Gaussian measure is constructed in a separable Hilbert space by two equivalent ways: (a) as a product measure, and (b) via a characteristic functional based on Minlos-Sazonov and Prokhorov’s theorem. The textbook contains Fernique’s theorem about exponential moments of Gaussian measure in Hilbert space and Feldman-Hajek dichotomy for Gaussian measures in Hilbert space.