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White noise analysis is an advanced stochastic calculus that has developed extensively since three decades ago. It has two main characteristics. One is the notion of generalized white noise functiona …

Quantum information is a developing multi-disciplinary field, with many exciting links to white noise theory. This connection is explored and presented in this work, which effectively bridges the gap …

A random field is a mathematical model of evolutional fluctuating complex systems parametrized by a multi-dimensional manifold like a curve or a surface. As the parameter varies, the random field car …

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. T …

This book provides the mathematical definition of white noise and gives its significance. White noise is in fact a typical class of idealized elemental (infinitesimal) random variables. Thus, we are …

This volume aims to return to the starting point of the fields of infinite dimensional analysis and quantum probability, fields that are growing rapidly at present, and to seriously attempt mutual in …