White Noise Distribution Theory

Author : Hui-Hsiung Kuo
Publisher : CRC Press
Page : 400 pages
File Size : 47,9 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351404303

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White Noise Distribution Theory by Hui-Hsiung Kuo Pdf

Learn the basics of white noise theory with White Noise Distribution Theory. This book covers the mathematical foundation and key applications of white noise theory without requiring advanced knowledge in this area. This instructive text specifically focuses on relevant application topics such as integral kernel operators, Fourier transforms, Laplacian operators, white noise integration, Feynman integrals, and positive generalized functions. Extremely well-written by one of the field's leading researchers, White Noise Distribution Theory is destined to become the definitive introductory resource on this challenging topic.

Author : Gopinath Kallianpur,Rajeeva L. Karandikar
Publisher : CRC Press
Page : 624 pages
File Size : 44,7 Mb
Release : 1988-01-01
Category : Mathematics
ISBN : 2881246850

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White Noise Theory of Prediction, Filtering and Smoothing by Gopinath Kallianpur,Rajeeva L. Karandikar Pdf

Based on the author’s own research, this book rigorously and systematically develops the theory of Gaussian white noise measures on Hilbert spaces to provide a comprehensive account of nonlinear filtering theory. Covers Markov processes, cylinder and quasi-cylinder probabilities and conditional expectation as well as predictio0n and smoothing and the varied processes used in filtering. Especially useful for electronic engineers and mathematical statisticians for explaining the systematic use of finely additive white noise theory leading to a more simplified and direct presentation.

Author : Nobuaki Obata
Publisher : Springer
Page : 195 pages
File Size : 53,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540484110

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White Noise Calculus and Fock Space by Nobuaki Obata Pdf

White Noise Calculus is a distribution theory on Gaussian space, proposed by T. Hida in 1975. This approach enables us to use pointwise defined creation and annihilation operators as well as the well-established theory of nuclear space.This self-contained monograph presents, for the first time, a systematic introduction to operator theory on fock space by means of white noise calculus. The goal is a comprehensive account of general expansion theory of Fock space operators and its applications. In particular,first order differential operators, Laplacians, rotation group, Fourier transform and their interrelations are discussed in detail w.r.t. harmonic analysis on Gaussian space. The mathematical formalism used here is based on distribution theory and functional analysis , prior knowledge of white noise calculus is not required.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 50,5 Mb
Release : 2024-04-28
Category : Electronic
ISBN : 9789814479172

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Stochastic Analysis: Classical and Quantum by Anonim Pdf

Author : Takeyuki Hida,Si Si
Publisher : World Scientific
Page : 216 pages
File Size : 53,5 Mb
Release : 2004
Category : Mathematics
ISBN : 9812565388

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An Innovation Approach to Random Fields by Takeyuki Hida,Si Si Pdf

A random field is a mathematical model of evolutional fluctuatingcomplex systems parametrized by a multi-dimensional manifold like acurve or a surface. As the parameter varies, the random field carriesmuch 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 elementalstochastic process with a basic and simple way of dependence, and thenexpress the given field as a function of the innovation. Theytherefore establish an infinite-dimensional stochastic calculus, inparticular a stochastic variational calculus. The analysis offunctions of the innovation is essentially infinite-dimensional. Theauthors use not only the theory of functional analysis, but also theirnew tools for the study

Author : Takeyuki Hida,Si Si
Publisher : World Scientific
Page : 204 pages
File Size : 48,7 Mb
Release : 2004-07-14
Category : Mathematics
ISBN : 9789814487924

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Innovation Approach To Random Fields, An: Application Of White Noise Theory by Takeyuki Hida,Si Si Pdf

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 calculus, in particular a stochastic variational calculus. The analysis of functions of the innovation is essentially infinite-dimensional. The authors use not only the theory of functional analysis, but also their new tools for the study.

Author : Takeyuki Hida,Si Si
Publisher : World Scientific
Page : 281 pages
File Size : 55,8 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812812049

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Lectures on White Noise Functionals by Takeyuki Hida,Si Si Pdf

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.

Author : Si Si
Publisher : World Scientific
Page : 268 pages
File Size : 49,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9789812836885

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Introduction to Hida Distributions by Si Si Pdf

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.

Author : D. Kannan,V. Lakshmikantham
Publisher : CRC Press
Page : 800 pages
File Size : 51,9 Mb
Release : 2001-10-23
Category : Mathematics
ISBN : 0824706609

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Handbook of Stochastic Analysis and Applications by D. Kannan,V. Lakshmikantham Pdf

An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.

Author : Hida Takeyuki,Streit Ludwig
Publisher : World Scientific
Page : 232 pages
File Size : 55,8 Mb
Release : 2017-03-10
Category : Mathematics
ISBN : 9789813220959

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Let Us Use White Noise by Hida Takeyuki,Streit Ludwig Pdf

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.

Author : Christopher C Bernido,Maria Victoria Carpio-bernido
Publisher : World Scientific
Page : 204 pages
File Size : 51,6 Mb
Release : 2014-11-27
Category : Mathematics
ISBN : 9789814569132

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Methods And Applications Of White Noise Analysis In Interdisciplinary Sciences by Christopher C Bernido,Maria Victoria Carpio-bernido Pdf

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.

Author : Andrei Y. Khrennikov
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 45,7 Mb
Release : 2013-03-09
Category : Science
ISBN : 9789401583565

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p-Adic Valued Distributions in Mathematical Physics by Andrei Y. Khrennikov Pdf

Numbers ... , natural, rational, real, complex, p-adic .... What do you know about p-adic numbers? Probably, you have never used any p-adic (nonrational) number before now. I was in the same situation few years ago. p-adic numbers were considered as an exotic part of pure mathematics without any application. I have also used only real and complex numbers in my investigations in functional analysis and its applications to the quantum field theory and I was sure that these number fields can be a basis of every physical model generated by nature. But recently new models of the quantum physics were proposed on the basis of p-adic numbers field Qp. What are p-adic numbers, p-adic analysis, p-adic physics, p-adic probability? p-adic numbers were introduced by K. Hensel (1904) in connection with problems of the pure theory of numbers. The construction of Qp is very similar to the construction of (p is a fixed prime number, p = 2,3,5, ... ,127, ... ). Both these number fields are completions of the field of rational numbers Q. But another valuation 1 . Ip is introduced on Q instead of the usual real valuation 1 . I· We get an infinite sequence of non isomorphic completions of Q : Q2, Q3, ... , Q127, ... , IR = Qoo· These fields are the only possibilities to com plete Q according to the famous theorem of Ostrowsky.

Author : Habib Ouerdiane
Publisher : World Scientific
Page : 314 pages
File Size : 53,7 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814295437

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Quantum Probability and Infinite Dimensional Analysis by Habib Ouerdiane Pdf

On the central extensions of the Heisenberg algebra / L. Accardi & A. Boukas -- Representations of the Lévy-Meixner oscillator algebra and the overcompleteness of the associated sequences of coherent states / A. Barhoumi, H. Ouerdiane & A. Riahi -- Some systems of dualities in white noise analysis / T. Hida -- Quantum white noise derivatives and associated differential equations for white noise operators / U.C. Ji & N. Obata -- The Gibbs conditioning principle for white noise distributions : interacting and non-interacting cases / F. Cipriano, S. Gheryani & H. Ouerdiane -- Markov triplets on CAR algebras / J. Pitrik -- Quantum Fokker-Planck models : limiting case in the Lindblad condition / F. Fagnola & L. Neumann -- Generalized Euler heat equation / A. Barhoumi, H. Ouerdiane & H. Rguigui -- On quantum De Finetti's theorems / V. Crismale & Y.G. Lu -- Kolmogorovian model for EPR-experiment / D. Avis [und weitere] -- Free white noise stochastic equation / L. Accardi, W. Ayed & H. Ouerdiane -- Lévy models robustness and sensitivity / F.E. Benth, G. Di Nunno & A. Khedher -- Quantum heat equation with quantum K-Gross Laplacian : solutions and integral representation / S. Horrigue & H. Ouerdiane -- On Marginal Markov processes of quantum quadratic stochastic processes / F. Mukhamedov -- On the applicability of multiplicative renormalization method for certain power functions / I. Kubo, H.-H. Kuo & S. Namli -- Convolution equation : solution and probabilistic representation / J.L. Da Silva, M. Erraoui & H. Ouerdiane -- From classical to quantum entropy production / F. Fagnola & R. Rebolledo -- Extending the set of quadratic exponential vectors / L. Accardi, A. Dhahri & M. Skeide -- On operator-parameter transforms based on nuclear algebra of entire functions and applications / A. Barhoumi [und weitere] -- Dissipative quantum annealing / D. de Falco, E. Pertoso & D. Tamascelli

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 50,9 Mb
Release : 2024-04-28
Category : Electronic
ISBN : 9789814465632

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Quantum Probability and Infinite Dimensional Analysis by Anonim Pdf

Author : Sergio Albeverio,Fritz Gesztesy
Publisher : American Mathematical Soc.
Page : 650 pages
File Size : 47,7 Mb
Release : 2000
Category : Mathematics
ISBN : 0821819607

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Stochastic Processes, Physics and Geometry: New Interplays. II by Sergio Albeverio,Fritz Gesztesy Pdf

This volume and Stochastic Processes, Physics and Geometry: New Interplays I present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, "Infinite Dimensional (Stochastic) Analysis and Quantum Physics", was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry. The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and noncommutative probability theory, integrable systems, quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas. Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional contributed papers. Members of the Canadian Mathematical Society may order at the AMS member price.