Methods And Applications Of White Noise Analysis In Interdisciplinary Sciences PDF Download
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Author: Christopher C Bernido
Publisher: World Scientific
ISBN: 9814569135
Category : Mathematics
Languages : en
Pages : 202
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Book Description
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: Christopher C Bernido
Publisher: World Scientific
ISBN: 9814569135
Category : Mathematics
Languages : en
Pages : 202
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Book Description
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: Christopher Caseñas Bernido
Publisher:
ISBN: 9789814569125
Category : MATHEMATICS
Languages : en
Pages :
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Book Description
Author: Luigi Accardi
Publisher: World Scientific
ISBN: 9813225475
Category : Mathematics
Languages : en
Pages : 243
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Book Description
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.
Author: Takeyuki Hida
Publisher: World Scientific
ISBN: 9814611565
Category :
Languages : en
Pages : 438
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Book Description
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.
Author: Takeyuki Hida
Publisher: World Scientific
ISBN: 9813220953
Category : Mathematics
Languages : en
Pages : 230
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Book Description
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
Publisher: Birkhäuser
ISBN: 3319072455
Category : Mathematics
Languages : en
Pages : 304
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Book Description
This volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields.
Author: Takeyuki Hida
Publisher: World Scientific Publishing Company Incorporated
ISBN: 9789810202422
Category : Brownian motion processes
Languages : en
Pages : 424
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Book Description
Author: Takeyuki Hida
Publisher: World Scientific
ISBN: 9812560521
Category : Technology & Engineering
Languages : en
Pages : 281
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Book Description
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: Takeyuki Hida
Publisher: Springer Science & Business Media
ISBN: 9780792322337
Category : Mathematics
Languages : en
Pages : 542
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Book Description
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.
Author: T. Hida
Publisher:
ISBN:
Category :
Languages : en
Pages : 424
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Book Description
