Many areas of applied mathematics call for an efficient calculus in infinite dimensions. This is most apparent in quantum physics and in all disciplines of science which describe natural phenomena by equations involving stochasticity. With this monograph we intend to provide a framework for analysis in infinite dimensions which is flexible enough to be applicable in many areas, and which on the other hand is intuitive and efficient. Whether or not we achieved our aim must be left to the judgment of the reader. This book treats the theory and applications of analysis and functional analysis in...

This text constitutes the proceedings of the first International Conference on Quantum Information, held at Meijo University, Japan in November 1997. Topics covered include teleportation of general quantum states, quantum computer and analysis and control of decoherence in spin system.

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...

This volume constitutes the proceedings of the Fourth International Conference on Quantum Information, held in Japan in 2001. Topics covered include: infinite dimensional harmonic analysis; white noise theory; complex Gaussian random fields; quantum information in space and time; and more.

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 carries much information and hence it has complex stochastic structure.

The authors of this book use an approach that is characteristic: namely, they first construct innovation, which is the most elemental stochastic process with a basic and simple way of dependence, and then express the given field as a function of the innovation. They therefore establish an infinite-dimensional stochastic...

This volume includes the proceedings of the Fifth Conference on Quantum Information held at Meijo University, Japan.

This volume includes papers by leading mathematicians in the fields of stochastic analysis, white noise theory and quantum information, together with their applications. The papers selected were presented at the International Conference on Stochastic Analysis: Classical and Quantum held at Meijo University, Nagoya, Japan from 1 to 5 November 2004. The large range of subjects covers the latest research in probability theory.

This monograph presents a framework for infinite dimensional analysis based on white noise. This approach, which has many areas of application is both intuitive and efficient. Among the concepts and structures generalized to an infinite dimensional setting in this book are: spaces of test and generalized functions, differential calculus, Laplacian and Fourier transforms and Dirichlet forms and their Markov processes. A multitude of concepts, such as Brownian motion functionals, falls into this framework. This book presents a simple, yet general theory of stochastic integration and also...

The use of probabilistic methods in the biological sciences has been so well established by now that mathematical biology is regarded by many as a distinct dis- cipline with its own repertoire of techniques. The purpose of the Workshop on sto- chastic methods in biology held at Nagoya University during the week of July 8-12, 1985, was to enable biologists and probabilists from Japan and the U. S. to discuss the latest developments in their respective fields and to exchange ideas on the ap- plicability of the more recent developments in stochastic process theory to problems in biology....

During the last fifty years, Gopinath Kallianpur has made extensive and significant contributions to diverse areas of probability and statistics, including stochastic finance, Fisher consistent estimation, non-linear prediction and filtering problems, zero-one laws for Gaussian processes and reproducing kernel Hilbert space theory, and stochastic differential equations in infinite dimensions. To honor Kallianpur's pioneering work and scholarly achievements, a number of leading experts have written research articles highlighting progress and new directions of research in these and related...