Lectures On White Noise Functionals
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Lectures On White Noise Functionals
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Author : Takeyuki Hida
language : en
Publisher: World Scientific
Release Date : 2008
Lectures On White Noise Functionals written by Takeyuki Hida and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Technology & Engineering categories.
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.
Lectures On White Noise Functionals
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Author : Takeyuki Hida
language : en
Publisher: World Scientific
Release Date : 2008-07-04
Lectures On White Noise Functionals written by Takeyuki Hida and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-04 with Mathematics categories.
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.
White Noise Analysis And Quantum Information
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Author : Ohya Masanori
language : en
Publisher: World Scientific
Release Date : 2017-08-29
White Noise Analysis And Quantum Information written by Ohya Masanori and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-29 with Language Arts & Disciplines categories.
This volume is to pique the interest of many researchers in the fields of infinite dimensional analysis and quantum probability. These fields have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. These fields are rather wide and are of a strongly interdisciplinary nature. For such a purpose, we strove to bridge among these interdisciplinary fields in our Workshop on IDAQP and their Applications that was held at the Institute for Mathematical Sciences, National University of Singapore from 3–7 March 2014. Readers will find that this volume contains all the exciting contributions by well-known researchers in search of new directions in these fields. Contents: Extensions of Quantum Theory Canonically Associated to Classical Probability Measures (Luigi Accardi)Hida Distribution Construction of Indefinite Metric (ϕp)d (d ≥ 4) Quantum Field Theory (Sergio Albeverio and Minoru W Yoshida)A Mathematical Realization of von Neumann's Measurement Scheme (Masanari Asano, Masanori Ohya and Yuta Yamamori)On Random White Noise Processes with Memory for Time Series Analysis (Christopher C Bernido and M Victoria Carpio-Bernido)Self-Repelling (Fractional) Brownian Motion: Results and Open Questions (Jinky Bornales and Ludwig Streit)Normal Approximation for White Noise Functionals by Stein's Method and Hida Calculus (Louis H Y Chen, Yuh-Jia Lee and Hsin-Hung Shih)Sensitive Homology Searching Based on MTRAP Alignment (Toshihide Hara and Masanori Ohya)Some of the Future Directions of White Noise Theory (Takeyuki Hida)Local Statistics for Random Selfadjoint Operators (Peter D Hislop and Maddaly Krishna)Multiple Markov Properties of Gaussian Processes and Their Control (Win Win Htay)Quantum Stochastic Differential Equations Associated with Square of Annihilation and Creation Processes (Un Cig Ji and Kalyan B Sinha)Itô Formula for Generalized Real and Complex White Noise Functionals (Yuh-Jia Lee)Quasi Quantum Quadratic Operators of 𝕄2(ℂ) (Farrukh Mukhamedov)New Noise Depending on the Space Parameter and the Concept of Multiplicity (Si Si)A Hysteresis Effect on Optical Illusion and Non-Kolmogorovian Probability Theory (Masanari Asano, Andrei Khrennikov, Masanori Ohya and Yoshiharu Tanaka)Note on Entropy-Type Complexity of Communication Processes (Noboru Watanabe) Readership: Mathematicians, physicists, biologists, and information scientists as well as advanced undergraduates, and graduate students studying in these fields. All researchers interested in the study of Quantum Information and White Noise Theory. Keywords: White Noise Analysis;Quantum Information;Quantum Probability;Bioinformatics;Genes;Adaptive Dynamics;Entanglement;Quantum Entropy;Non-Kolmogorovian Probability;Infinite Dimensional AnalysisReview: Key Features: Mainly focused on quantum information theory and white noise analysis in line with the fields of infinite dimensional analysis and quantum probabilityWhite noise analysis is in a leading position of the analysis on modern stochastic analysis, and this volume contains contributions to the development of these new exciting directions
White Noise Analysis Mathematics And Applications
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Author : Takeyuki Hida
language : en
Publisher: World Scientific
Release Date : 1990-06-30
White Noise Analysis Mathematics And Applications written by Takeyuki Hida and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-06-30 with categories.
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.
A White Noise Theory Of Infinite Dimensional Calculus
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Author : Takeyuki Hida
language : en
Publisher:
Release Date : 1989
A White Noise Theory Of Infinite Dimensional Calculus written by Takeyuki Hida and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
Sections 1-4 are based on those three lectures with somewhat more attention devoted to the space of generalized white noise functionals. What is described here are mostly survey articles, though some state-of-the-art results are added, while Section 5 involves a new approach to the study of Gaussian random fields. This topic is exactly what the author wished to propose at the colloquium. What is going to be presented here is, of course, far from a general theory; however it is his hope that this attempt would be the very first step towards the study of Gaussian random fields using variational calculus. Contents: White noise; Generalized functionals; Rotation group and harmonic analysis; Applications to Physics; Gaussian random fields. Keywords: Statistic processes. (kr).
Let Us Use White Noise
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Author : Hida Takeyuki
language : en
Publisher: World Scientific
Release Date : 2017-03-10
Let Us Use White Noise written by Hida Takeyuki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-10 with Mathematics categories.
Why should we use white noise analysis? Well, one reason of course is that it fills that earlier gap in the tool kit. As Hida would put it, white noise provides us with a useful set of independent coordinates, parametrized by "time". And there is a feature which makes white noise analysis extremely user-friendly. Typically the physicist — and not only he — sits there with some heuristic ansatz, like e.g. the famous Feynman "integral", wondering whether and how this might make sense mathematically. In many cases the characterization theorem of white noise analysis provides the user with a sweet and easy answer. Feynman's "integral" can now be understood, the "It's all in the vacuum" ansatz of Haag and Coester is now making sense via Dirichlet forms, and so on in many fields of application. There is mathematical finance, there have been applications in biology, and engineering, many more than we could collect in the present volume. Finally, there is one extra benefit: when we internalize the structures of Gaussian white noise analysis we will be ready to meet another close relative. We will enjoy the important similarities and differences which we encounter in the Poisson case, championed in particular by Y Kondratiev and his group. Let us look forward to a companion volume on the uses of Poisson white noise. The present volume is more than a collection of autonomous contributions. The introductory chapter on white noise analysis was made available to the other authors early on for reference and to facilitate conceptual and notational coherence in their work.
White Noise Functionals Of Gaussian And Other Noises
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Author : Takeyuki Hida
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016-06-30
White Noise Functionals Of Gaussian And Other Noises written by Takeyuki Hida and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-30 with Mathematics categories.
We propose a new direction for stochastic analysis. Starting with a noise which is a system of i.i.d. idealized elemental random variables, we form polynomials in the noise and come to the space of generalized functionals of the noise with special emphasis on the Gaussian noise. New tools of analyzing these functionals are introduced. We further establish a harmonic analysis arising from the infinite dimensional rotation group which plays significant roles in white noise analysis. Many applications, in particular to quantum dynamics, have been shown.Functionals of other kind of noises are discussed. As a new approach, we discuss functionals of a space noise. There one can find similarity and dissimilarity as well as duality to the analysis of Poisson noise functionals.
Methods And Applications Of White Noise Analysis In Interdisciplinary Sciences
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Author : Christopher C Bernido
language : en
Publisher: World Scientific
Release Date : 2014-11-27
Methods And Applications Of White Noise Analysis In Interdisciplinary Sciences written by Christopher C Bernido and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-27 with Mathematics categories.
Analysis, modeling, and simulation for better understanding of diverse complex natural and social phenomena often require powerful tools and analytical methods. Tractable approaches, however, can be developed with mathematics beyond the common toolbox. This book presents the white noise stochastic calculus, originated by T Hida, as a novel and powerful tool in investigating physical and social systems. The calculus, when combined with Feynman's summation-over-all-histories, has opened new avenues for resolving cross-disciplinary problems. Applications to real-world complex phenomena are further enhanced by parametrizing non-Markovian evolution of a system with various types of memory functions. This book presents general methods and applications to problems encountered in complex systems, scaling in industry, neuroscience, polymer physics, biophysics, time series analysis, relativistic and nonrelativistic quantum systems.
White Noise
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Author : Takeyuki Hida
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-03-31
White Noise written by Takeyuki Hida and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-03-31 with Mathematics categories.
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 discusses construction quantum field theory and Feynman's functional integration. This volume will be of interest to mathematicians and scientists who use stochastic methods in their research. The book will be of particular value to mathematicians in probability theory, functional analysis, measure theory, potential theory, as well as to physicists and scientists in engineering.
Introduction To Hida Distributions
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Author : Si Si
language : en
Publisher: World Scientific
Release Date : 2012
Introduction To Hida Distributions written by Si Si and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
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 naturally led to have functionals of such elemental random variables that is white noise. This book analyzes those functionals of white noise, particularly the generalized ones called Hida distributions, and highlights some interesting future directions. The main part of the book involves infinite dimensional differential and integral calculus based on the variable which is white noise.The present book can be used as a supplementary book to Lectures on White Noise Functionals published in 2008, with detailed background provided.