Si Si

T Hida

' 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 functionals, the introduction of which is oriented by the line of advanced analysis, and they have made much contribution to the fields in science enormously. The other characteristic is that the white noise analysis has an aspect of infinite dimensional harmonic analysis arising from the infinite dimensional rotation group. With the help of this rotation group, the white noise analysis has explored new areas of mathematics and has extended the fields of applications. Contents:Generalized White Noise FunctionalsElemental Random Variables and Gaussian ProcessesLinear Processes and Linear FieldsHarmonic Analysis Arising from Infinite Dimensional Rotation GroupComplex White Noise and Infinite Dimensional Unitary GroupCharacterization of Poisson NoiseInnovation TheoryVariational Calculus for Random Fields and Operator FieldsFour Notable Roads to Quantum Dynamics Readership: Researchers in probability and statistics and mathematical physics. Keywords:White Noise;Poisson Noise;Stochastic Analysis;Innovation;Random Field and Its Variation;Random Complexity;Infinite Dimensional Rotation GroupKey Features:A tightly edited distillation of a quarter of century of work by many scientistsContains the original ideas with some interpretation of development to recent worksCommentaries on each of the topics coveredReviews:“This monograph is a valuable guide to the world of white noise analysis originated by Hida. It is full of ideas, essentials and philosophy about why analysis based upon the white noise is needed, what the white noise functionals are, how to handle stochastic processes on an applicational basis to quantum physics, how to find a natural way to formulate the infinite-dimensional harmonic analysis, etc. This book is recommendable not only to ambitious graduate students in probability or applied analysis in a broad sense, but also to researchers who work on infinite-dimensional analysis or mathematical physics, as well as to any readers who are interested in white noise analysis.”Mathematical Reviews '

Lectures on White Noise Functionals

S Albeverio

P Blanchard

L Ferreira

Y Kondratiev

R Vilela Mendes

In October 1998 a conference was held in Lisbon to celebrate Ludwig Streit's 60th birthday. This book collects some of the papers presented at the conference as well as other essays contributed by the many friends and collaborators who wanted to honor Ludwig Streit's scientific career and personality. The contributions cover many aspects of contemporary mathematical physics. Of particular importance are new results on infinite-dimensional stochastic analysis and its applications to a wide range of physical domains. List of Contributors: S Albeverio, T Hida, L Accardi, I Ya Aref'eva, I V Volovich; A Daletskii, Y Kondratiev, W Karwowski, N Asai, I Kubo, H-H Kuo, J Beckers, Ph Blanchard, G F Dell'Antonio, D Gandolfo, M Sirugue-Collin, A Bohm, H Kaldass, D Bollé, G Jongen, G M Shim, J Bornales, C C Bernido, M V Carpio-Bernido, G Burdet, Ph Combe, H Nencka, P Cartier, C DeWitt-Morette, H Ezawa, K Nakamura, K Watanabe, Y Yamanaka, R Figari, F Gesztesy, H Holden, R Gielerak, G A Goldin, Z Haba, M-O Hongler, Y Hu, B Oksendal, A Sulem, J R Klauder, C B Lang, V I Man'ko, H Ouerdiane, J Potthoff, E Smajlovic, M Röckner, E Scacciatelli, J L Silva, J Stochel, F H Szafraniec, L Vázquez, D N Kozakevich, S Jiménez, V R Vieira, P D Sacramento, R Vilela Mendes, D Volný, P Samek. Contents:Some Themes of the Scientific Work of Ludwig Streit (S Albeverio)Nonlinear Lie Algebras in Quantum Physics and Their Interest in Quantum Field Theory (J Beckers)Rigged Hilbert Space Resonances and Time Asymmetric Quantum Mechanics (A Bohm & H Kaldass)The Relativistic Aharonov-Bohm-Coulomb Problem: A Path Integral Solution (J Bornales et al.)Time Dependent and Nonlinear Point Interactions (R Figari)Stochastic Processes and the Feynman Integral (Z Haba)Nonrenormalizability and Nontriviality (J R Klauder)On the Spectrum of Lattice Dirac Operators (C B Lang)External and Internal Geometry on Configuration Spaces (J L Silva)Spinor Description of a General Spin-J System (V R Vieira & P D Sacramento)and other papers Readership: Theoretical physicists, mathematical physicists, mathematicians, computer scientists and economists. Keywords:

Essays in Honour of Ludwig Streit

Mathematical Physics and Stochastic Analysis

K SaitÃ´

Contents:Recognition and Teleportation (M Ohya et al.)Quantum Information and Spacetime Structure (I V Volovich)On Gaussian and Poisson White Noises (N Asai)Renormalization, Orthogonalization, and Generating Functions (N Asai et al.)Insider Trading in Continuous Time (E Barucci et al.)Existence, Uniqueness, Consistency and Dependency on Diffusion Coefficients of Generalized Solutions of Nonlinear Diffusion Equations in Colombeau's Algebra (H Deguchi)On Mathematical Treatment of Quantum Communication Gate on Fock Space (W Freudenberg et al.)A Frontier of White Noise Analysis (T Hida)An Interacting Fock Space with Periodic Jacobi Parameter Obtained from Regular Graphs in Large Scale Limit (A Hora & N Obata)Error Exponents of Codings for Stationary Gaussian Channels (S Ihara)White Noise Analysis on Classical Wiener Space Revisited (Y-J Lee & H-H Shih)Fractional Brownian Motions and the Lévy Laplacian (K Nishi et al.)Jump Finding of a Stable Process (Si Si et al.)On Entropy Production of a One-Dimensional Lattice Conductor (S Tasaki) Readership: Researchers in probability & statistics, mathematical physics, functional analysis and mathematical biology. Keywords:Quantum Information;White Noise Analysis;Fock Space;Classical Wiener Space;Brownian Motion

Quantum Information V

H H Kuo

J Potthoff

L Streit

This proceedings contains articles on white noise analysis and related subjects. Applications in various branches of science are also discussed. White noise analysis stems from considering the time derivative of Brownian motion (“white noise”) as the basic ingredient of an infinite dimensional calculus. It provides a powerful mathematical tool for research fields such as stochastic analysis, potential theory in infinite dimensions and quantum field theory. Contents:Exponential Estimates of Large Devivation Type for Itô Processes in Hilbert Space (P L Chow)Multilevel Branching Systems (D A Dawson et al)White Noise Analysis - An Overview (T Hida and J Potthoff)Generalized Functionals on ( R∞, B∞, N∞ ) (K Itô)White Noise Analysis as a Tool in Computing Feynman Integrals (D C Khandeka)White Noise from a Hilbert Space Point of View (P A Meyer)Anticipating Stochastic Calculus and Applications (D Ocone)Hierarchy of Noise Production in Living Cells (F Oosawa)Linear Kernels Associated with Distributions of Stochastic Processes (W Smolenski)Positive Generalized Brownian Functionals (Y Yokoi)and others Readership: Mathematicians and mathematical physicists.

Mathematics and Applications

White Noise Analysis

T Hida

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