Selected Papers of Takeyuki Hida

The topics discussed in this book can be classified into three parts: (i) Gaussian processes. The most general and in fact final representation theory of Gaussian processes is included in this book. This theory is still referred to often and its developments are discussed. (ii) White noise analysis. This book includes the notes of the series of lectures delivered in 1975 at Carleton University in Ottawa. They describe the very original idea of introducing the notion of generalized Brownian functionals (nowadays called “generalized white noise functionals”, and sometimes “Hida distribution”. (iii) Variational calculus for random fields. This topic will certainly represent one of the driving research lines for probability theory in the next century, as can be seen from several papers in this volume. Contents:General Theory of White Noise FunctionalsGaussian and Other ProcessesInfinite Dimensional Harmonic Analysis and Rotation GroupQuantum TheoryFeynman Integrals and Random FieldsVariational Calculus and Random FieldsApplication to Biology Readership: Graduate students and researchers in the fields of probability theory, functional analysis, statistics and theoretical physics. Keywords:White Noise;Gaussian;Brownian Motion;Lévy Process;Canonical Representation;Stochastic Infinitesimal Equation;Generalized Functional;Innovation;Multiple Markov;Random FieldReviews:“This collection of papers is a tribute to one of the great researchers within stochastic analysis, Takeyuki Hida … An interesting appendix, however, is the collection of remarks at the end of the book … These remarks serve to put the various papers into perspective, and represent a valuable contribution.”Mathematical Reviews