Download or read book Lectures on White Noise Functionals written by Takeyuki Hida and published by World Scientific. This book was released on 2008 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lectures On White Noise Functionals written by Takeyuki Hida and published by World Scientific. This book was released on 2008-07-04 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book White Noise Analysis And Quantum Information written by Luigi Accardi and published by World Scientific. This book was released on 2017-08-29 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book White Noise Analysis Mathematics And Applications written by Takeyuki Hida and published by World Scientific. This book was released on 1990-06-30 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Let Us Use White Noise written by Takeyuki Hida and published by World Scientific. This book was released on 2017-03-10 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A White Noise Theory of Infinite Dimensional Calculus written by Takeyuki Hida and published by . This book was released on 1989 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book White Noise Functionals of Gaussian and Other Noises written by Takeyuki Hida and published by World Scientific Publishing Company. This book was released on 2016-06-30 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Methods And Applications Of White Noise Analysis In Interdisciplinary Sciences written by Christopher C Bernido and published by World Scientific. This book was released on 2014-11-27 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book White Noise written by Takeyuki Hida and published by Springer Science & Business Media. This book was released on 1993-03-31 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book White Noise Distribution Theory written by Hui-Hsiung Kuo and published by CRC Press. This book was released on 2018-05-04 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stochastic Processes written by Stamatis Cambanis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume celebrates the many contributions which Gopinath Kallianpur has made to probability and statistics. It comprises 40 chapters which taken together survey the wide sweep of ideas which have been influenced by Professor Kallianpur's writing and research.
Download or read book Quantum Probability and Infinite Dimensional Analysis written by Habib Ouerdiane and published by World Scientific. This book was released on 2010 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Quantum Probability And Infinite Dimensional Analysis Proceedings Of The 29th Conference written by Habib Ouerdiane and published by World Scientific. This book was released on 2010-02-10 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the proceedings of the 29th Conference on Quantum Probability and Infinite Dimensional Analysis, which was held in Hammamet, Tunisia.
Download or read book Quantum Bio informatics III written by Luigi Accardi and published by World Scientific. This book was released on 2010 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical and quantum conditioning : mathematical and information theoretical aspects / L. Accardi -- Dynamics and potentials / F. Araki -- Kossakowski-Ohya teleportation scheme and its applications / M. Asano, M. Ohya and Y. Tanaka -- Utility and value of information in cognitive science, biology and quantum theory / R.V. Belavkin -- Spectral properties of entanglement witnesses and positive maps / D. Chruściński -- Quantum entanglement and multipartite symmetric states / D. Chruściński -- On a quantum model of brain activities / K.-H. Fichtner [und weitere] -- Some of the recent topics in white noise theory / T. Hida -- Note on generalized white noise functionals / T. Hida -- On estimation of the position distribution of the ideal Bose gas / K.-H. Fichtner, K. Inoue and M. Ohya -- On generalization of quantum mutual entropy by using liftings / S. Iriyama and M. Ohya -- A new approach to stroboscopic tomography of open systems / A. Jamiolkowski -- An introduction to frames and their applications to quantum optics / A. Jamiolkowski -- Memory in a nonlocally damped oscillator / D. Chruściński and J. Jurkowski -- An introduction to quantization of dissipative systems. The damped harmonic oscillator case / J. Jurkowski -- Classical and quantum probability for biologists - introduction / A. Khrennikov -- 2-adic degeneration of the genetic code and energy of binding of codons / A. Yu. Khrennikov and S.V. Kozyrev -- On positive maps; PPT states and entanglement / W.A. Majewski -- Detecting entanglement in spin lattice models / M. Michalski -- How to detect entanglement in quantum systems / M. Michalskii -- Tunneling study on high-T[symbol] superconductors / M. Minematsu, S. Kawashima and N. Miyakawa -- Quantum dynamics of superconducting qubit readout with a driven nonlinear Josephson oscillator / H. Nakano -- Roles of asymptotic condition and S-matrix as micro-macro duality in QFT / I. Ojima -- Gaussian Markov triplets / D. Petz and J. Pitrik -- pre-mRNA introns as a model for cryptographic algorithm : theory and experiments / M. Regoli -- Duality arising from multiple Markov Gaussian processes / Si Si and W.W. Htay -- Novel computational approaches to drug discovery / J. Skolnick and M. Brylinski -- Feynman type formulae for quantum evolution and diffusion on manifolds and graphs / O.G. Smolyanov -- Poisson noise and the dynamics of infinite particle systems / L. Streit -- Replica-exchange molecular dynamics simulations of Amyloid precursor protein dimer in membrane / N. Miyashita and Y. Sugita -- Comparison of square contingency tables using measure of departure from marginal homogeneity / K. Tahata [und weitere] -- On the statics for micro-array data analysis / T. Urushibara [und weitere] -- Functional mechanics and time irreversibility problem / I.V. Volovich -- Regulatory networks : inferring functional relationships through co-expression / D. Wanke [und weitere] -- On entropies of quantum dynamical systems / N. Watanabe -- Significant improvement of sequence alignment can be done by considering transition probability between two consecutive pairs of residues / T. Ham, K. Sato and M. Ohya -- A computational approach to explore protein translocation through Type III secretion apparatus / T. Rathinavelan and W. Im -- Carbon nanotubes for building blocks of quantum computing devices / K. Ishibashi [und weitere] -- In silico analysis for the study of botulinum toxin structure / T. Suzuki and S. Miyazaki -- Gene discovery methods from large-scale gene expression data / A. Shimizu and K. Yano
Download or read book Quantum Information IV written by Takeyuki Hida and published by World Scientific. This book was released on 2002 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation. ...study on the Power of Potential fluctuation in living cells...some properties of measure-valued processes with singular branching rate and other papers.
Download or read book White Noise on Bialgebras written by Michael Schürmann and published by Springer. This book was released on 2006-11-15 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic processes with independent increments on a group are generalized to the concept of "white noise" on a Hopf algebra or bialgebra. The main purpose of the book is the characterization of these processes as solutions of quantum stochastic differential equations in the sense of R.L. Hudsonand K.R. Parthasarathy. The notes are a contribution to quantum probability but they are also related to classical probability, quantum groups, and operator algebras. The Az ma martingales appear as examples of white noise on a Hopf algebra which is a deformation of the Heisenberg group. The book will be of interest to probabilists and quantum probabilists. Specialists in algebraic structures who are curious about the role of their concepts in probablility theory as well as quantum theory may find the book interesting. The reader should havesome knowledge of functional analysis, operator algebras, and probability theory.
Download or read book Recent Developments in Infinite Dimensional Analysis and Quantum Probability written by Luigi Accardi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent Developments in Infinite-Dimensional Analysis and Quantum Probability is dedicated to Professor Takeyuki Hida on the occasion of his 70th birthday. The book is more than a collection of articles. In fact, in it the reader will find a consistent editorial work, devoted to attempting to obtain a unitary picture from the different contributions and to give a comprehensive account of important recent developments in contemporary white noise analysis and some of its applications. For this reason, not only the latest results, but also motivations, explanations and connections with previous work have been included. The wealth of applications, from number theory to signal processing, from optimal filtering to information theory, from the statistics of stationary flows to quantum cable equations, show the power of white noise analysis as a tool. Beyond these, the authors emphasize its connections with practically all branches of contemporary probability, including stochastic geometry, the structure theory of stationary Gaussian processes, Neumann boundary value problems, and large deviations.
