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Tools For Infinite Dimensional Analysis
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Book Synopsis Tools for Infinite Dimensional Analysis by : Jeremy J. Becnel
Download or read book Tools for Infinite Dimensional Analysis written by Jeremy J. Becnel and published by CRC Press. This book was released on 2020-12-28 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past six decades, several extremely important fields in mathematics have been developed. Among these are Itô calculus, Gaussian measures on Banach spaces, Malliavan calculus, and white noise distribution theory. These subjects have many applications, ranging from finance and economics to physics and biology. Unfortunately, the background information required to conduct research in these subjects presents a tremendous roadblock. The background material primarily stems from an abstract subject known as infinite dimensional topological vector spaces. While this information forms the backdrop for these subjects, the books and papers written about topological vector spaces were never truly written for researchers studying infinite dimensional analysis. Thus, the literature for topological vector spaces is dense and difficult to digest, much of it being written prior to the 1960s. Tools for Infinite Dimensional Analysis aims to address these problems by providing an introduction to the background material for infinite dimensional analysis that is friendly in style and accessible to graduate students and researchers studying the above-mentioned subjects. It will save current and future researchers countless hours and promote research in these areas by removing an obstacle in the path to beginning study in areas of infinite dimensional analysis. Features Focused approach to the subject matter Suitable for graduate students as well as researchers Detailed proofs of primary results
Book Synopsis Tools for Infinite Dimensional Analysis by : Jeremy J. Becnel
Download or read book Tools for Infinite Dimensional Analysis written by Jeremy J. Becnel and published by CRC Press. This book was released on 2020-12-21 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past six decades, several extremely important fields in mathematics have been developed. Among these are Itô calculus, Gaussian measures on Banach spaces, Malliavan calculus, and white noise distribution theory. These subjects have many applications, ranging from finance and economics to physics and biology. Unfortunately, the background information required to conduct research in these subjects presents a tremendous roadblock. The background material primarily stems from an abstract subject known as infinite dimensional topological vector spaces. While this information forms the backdrop for these subjects, the books and papers written about topological vector spaces were never truly written for researchers studying infinite dimensional analysis. Thus, the literature for topological vector spaces is dense and difficult to digest, much of it being written prior to the 1960s. Tools for Infinite Dimensional Analysis aims to address these problems by providing an introduction to the background material for infinite dimensional analysis that is friendly in style and accessible to graduate students and researchers studying the above-mentioned subjects. It will save current and future researchers countless hours and promote research in these areas by removing an obstacle in the path to beginning study in areas of infinite dimensional analysis. Features Focused approach to the subject matter Suitable for graduate students as well as researchers Detailed proofs of primary results
Book Synopsis An Introduction to Infinite-Dimensional Analysis by : Giuseppe Da Prato
Download or read book An Introduction to Infinite-Dimensional Analysis written by Giuseppe Da Prato and published by Springer Science & Business Media. This book was released on 2006-08-25 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate basic stochastic dynamical systems and Markov semi-groups, paying attention to their long-time behavior.
Book Synopsis Infinite Dimensional Stochastic Analysis by : Hui-Hsiung Kuo
Download or read book Infinite Dimensional Stochastic Analysis written by Hui-Hsiung Kuo and published by World Scientific. This book was released on 2008 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains current work at the frontiers of research in infinite dimensional stochastic analysis. It presents a carefully chosen collection of articles by experts to highlight the latest developments in white noise theory, infinite dimensional transforms, quantum probability, stochastic partial differential equations, and applications to mathematical finance. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians. Sample Chapter(s). Complex White Noise and the Infinite Dimensional Unitary Group (425 KB). Contents: Complex White Noise and the Infinite Dimensional Unitary Group (T Hida); Complex It Formulas (M Redfern); White Noise Analysis: Background and a Recent Application (J Becnel & A N Sengupta); Probability Measures with Sub-Additive Principal SzegAOCoJacobi Parameters (A Stan); Donsker''s Functional Calculus and Related Questions (P-L Chow & J Potthoff); Stochastic Analysis of Tidal Dynamics Equation (U Manna et al.); Adapted Solutions to the Backward Stochastic NavierOCoStokes Equations in 3D (P Sundar & H Yin); Spaces of Test and Generalized Functions of Arcsine White Noise Formulas (A Barhoumi et al.); An Infinite Dimensional Fourier-Mehler Transform and the L(r)vy Laplacian (K Saito & K Sakabe); The Heat Operator in Infinite Dimensions (B C Hall); Quantum Stochastic Dilation of Symmetric Covariant Completely Positive Semigroups with Unbounded Generator (D Goswami & K B Sinha); White Noise Analysis in the Theory of Three-Manifold Quantum Invariants (A Hahn); A New Explicit Formula for the Solution of the BlackOCoMertonOCoScholes Equation (J A Goldstein et al.); Volatility Models of the Yield Curve (V Goodman). Readership: Graduate-level researchers in stochastic analysis, mathematical physics and financial mathematic
Book Synopsis Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory by : Palle Jorgensen
Download or read book Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory written by Palle Jorgensen and published by World Scientific. This book was released on 2021-01-15 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to make available to beginning graduate students, and to others, some core areas of analysis which serve as prerequisites for new developments in pure and applied areas. We begin with a presentation (Chapters 1 and 2) of a selection of topics from the theory of operators in Hilbert space, algebras of operators, and their corresponding spectral theory. This is a systematic presentation of interrelated topics from infinite-dimensional and non-commutative analysis; again, with view to applications. Chapter 3 covers a study of representations of the canonical commutation relations (CCRs); with emphasis on the requirements of infinite-dimensional calculus of variations, often referred to as Ito and Malliavin calculus, Chapters 4-6. This further connects to key areas in quantum physics.
Book Synopsis Quantum Probability and Related Topics by : L. Accardi
Download or read book Quantum Probability and Related Topics written by L. Accardi and published by World Scientific. This book was released on 1993 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Probability and Related Topics is a series of volumes based on material discussed at the various QP conferences. It aims to provide an update on the rapidly growing field of classical probability, quantum physics and functional analysis.
Book Synopsis Infinite Dimensional Optimization and Control Theory by : Hector O. Fattorini
Download or read book Infinite Dimensional Optimization and Control Theory written by Hector O. Fattorini and published by Cambridge University Press. This book was released on 1999-03-28 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: Treats optimal problems for systems described by ODEs and PDEs, using an approach that unifies finite and infinite dimensional nonlinear programming.
Book Synopsis Techniques of Variational Analysis by : Jonathan Borwein
Download or read book Techniques of Variational Analysis written by Jonathan Borwein and published by Springer Science & Business Media. This book was released on 2006-06-18 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Borwein is an authority in the area of mathematical optimization, and his book makes an important contribution to variational analysis Provides a good introduction to the topic
Book Synopsis Fundamentals of Infinite Dimensional Representation Theory by : Raymond C. Fabec
Download or read book Fundamentals of Infinite Dimensional Representation Theory written by Raymond C. Fabec and published by CRC Press. This book was released on 2018-10-03 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite dimensional representation theory blossomed in the latter half of the twentieth century, developing in part with quantum mechanics and becoming one of the mainstays of modern mathematics. Fundamentals of Infinite Dimensional Representation Theory provides an accessible account of the topics in analytic group representation theory and operator algebras from which much of the subject has evolved. It presents new and old results in a coherent and natural manner and studies a number of tools useful in various areas of this diversely applied subject. From Borel spaces and selection theorems to Mackey's theory of induction, measures on homogeneous spaces, and the theory of left Hilbert algebras, the author's self-contained treatment allows readers to choose from a wide variety of topics and pursue them independently according to their needs. Beyond serving as both a general reference and as a text for those requiring a background in group-operator algebra representation theory, for careful readers, this monograph helps reveal not only the subject's utility, but also its inherent beauty.
Book Synopsis Stability of Finite and Infinite Dimensional Systems by : Michael I. Gil'
Download or read book Stability of Finite and Infinite Dimensional Systems written by Michael I. Gil' and published by Springer Science & Business Media. This book was released on 1998-09-30 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of Stability of Finite and Infinite Dimensional Systems is to provide new tools for specialists in control system theory, stability theory of ordinary and partial differential equations, and differential-delay equations. Stability of Finite and Infinite Dimensional Systems is the first book that gives a systematic exposition of the approach to stability analysis which is based on estimates for matrix-valued and operator-valued functions, allowing us to investigate various classes of finite and infinite dimensional systems from the unified viewpoint. This book contains solutions to the problems connected with the Aizerman and generalized Aizerman conjectures and presents fundamental results by A. Yu. Levin for the stability of nonautonomous systems having variable real characteristic roots. Stability of Finite and Infinite Dimensional Systems is intended not only for specialists in stability theory, but for anyone interested in various applications who has had at least a first-year graduate-level course in analysis.
Book Synopsis Mathematical Foundations of Infinite-Dimensional Statistical Models by : Evarist Giné
Download or read book Mathematical Foundations of Infinite-Dimensional Statistical Models written by Evarist Giné and published by Cambridge University Press. This book was released on 2021-03-25 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: In nonparametric and high-dimensional statistical models, the classical Gauss–Fisher–Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a final chapter the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions. Winner of the 2017 PROSE Award for Mathematics.
Author :Edited by Paul F. Kisak Publisher :Createspace Independent Publishing Platform ISBN 13 :9781523323999 Total Pages :190 pages Book Rating :4.3/5 (239 download)
Book Synopsis Hilbert Space by : Edited by Paul F. Kisak
Download or read book Hilbert Space written by Edited by Paul F. Kisak and published by Createspace Independent Publishing Platform. This book was released on 2016-01-07 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions. A Hilbert space is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured. Furthermore, Hilbert spaces are complete: there are enough limits in the space to allow the techniques of calculus to be used. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as infinite-dimensional function spaces. The earliest Hilbert spaces were studied from this point of view in the first decade of the 20th century by David Hilbert, Erhard Schmidt, and Frigyes Riesz. They are indispensable tools in the theories of partial differential equations, quantum mechanics, Fourier analysis (which includes applications to signal processing and heat transfer)-and ergodic theory, which forms the mathematical underpinning of thermodynamics. John von Neumann coined the term Hilbert space for the abstract concept that underlies many of these diverse applications. The success of Hilbert space methods ushered in a very fruitful era for functional analysis. Apart from the classical Euclidean spaces, examples of Hilbert spaces include spaces of square-integrable functions, spaces of sequences, Sobolev spaces consisting of generalized functions, and Hardy spaces of holomorphic functions. This book gives a mathematical overview of the definition and use of Hilbert Space.
Book Synopsis Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective by : René Carmona
Download or read book Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective written by René Carmona and published by Springer Science & Business Media. This book was released on 2007-05-22 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the mathematical issues that arise in modeling the interest rate term structure by casting the interest-rate models as stochastic evolution equations in infinite dimensions. The text includes a crash course on interest rates, a self-contained introduction to infinite dimensional stochastic analysis, and recent results in interest rate theory. From the reviews: "A wonderful book. The authors present some cutting-edge math." --WWW.RISKBOOK.COM
Book Synopsis Ergodicity for Infinite Dimensional Systems by : Giuseppe Da Prato
Download or read book Ergodicity for Infinite Dimensional Systems written by Giuseppe Da Prato and published by Cambridge University Press. This book was released on 1996-05-16 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the only book on stochastic modelling of infinite dimensional dynamical systems.
Book Synopsis Stochastic Equations in Infinite Dimensions by : Da Prato Guiseppe
Download or read book Stochastic Equations in Infinite Dimensions written by Da Prato Guiseppe and published by . This book was released on 2013-11-21 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to give a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. These are a generalization of stochastic differential equations as introduced by Ito and Gikham that occur, for instance, when describing random phenomena that crop up in science and engineering, as well as in the study of differential equations. The book is divided into three parts. In the first the authors give a self-contained exposition of the basic properties of probability measure on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof. The book ends with a comprehensive bibliography that will contribute to the book's value for all working in stochastic differential equations."
Author :Charalambos D. Aliprantis Publisher :Springer Science & Business Media ISBN 13 :9783540326960 Total Pages :732 pages Book Rating :4.3/5 (269 download)
Book Synopsis Infinite Dimensional Analysis by : Charalambos D. Aliprantis
Download or read book Infinite Dimensional Analysis written by Charalambos D. Aliprantis and published by Springer Science & Business Media. This book was released on 2007-05-02 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a study of modern functional analysis. It is intended for the student or researcher who could benefit from functional analytic methods, but does not have an extensive background and does not plan to make a career as a functional analyst.
Book Synopsis Infinite Dimensional Analysis, Quantum Probability and Applications by : Luigi Accardi
Download or read book Infinite Dimensional Analysis, Quantum Probability and Applications written by Luigi Accardi and published by Springer Nature. This book was released on 2022-10-04 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume gathers selected, peer-reviewed papers presented at the 41st International Conference on Infinite Dimensional Analysis, Quantum Probability and Related Topics (QP41) that was virtually held at the United Arab Emirates University (UAEU) in Al Ain, Abu Dhabi, from March 28th to April 1st, 2021. The works cover recent developments in quantum probability and infinite dimensional analysis, with a special focus on applications to mathematical physics and quantum information theory. Covered topics include white noise theory, quantum field theory, quantum Markov processes, free probability, interacting Fock spaces, and more. By emphasizing the interconnection and interdependence of such research topics and their real-life applications, this reputed conference has set itself as a distinguished forum to communicate and discuss new findings in truly relevant aspects of theoretical and applied mathematics, notably in the field of mathematical physics, as well as an event of choice for the promotion of mathematical applications that address the most relevant problems found in industry. That makes this volume a suitable reading not only for researchers and graduate students with an interest in the field but for practitioners as well.
