An Introduction To Infinite Dimensional Analysis

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An Introduction To Infinite Dimensional Analysis

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Author : Giuseppe Da Prato
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-25

An Introduction To Infinite Dimensional Analysis written by Giuseppe Da Prato 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 2006-08-25 with Mathematics categories.

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.

Introduction To Infinite Dimensional Stochastic Analysis

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Author : Zhi-yuan Huang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Introduction To Infinite Dimensional Stochastic Analysis written by Zhi-yuan Huang 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 2012-12-06 with Mathematics categories.

The infinite dimensional analysis as a branch of mathematical sciences was formed in the late 19th and early 20th centuries. Motivated by problems in mathematical physics, the first steps in this field were taken by V. Volterra, R. GateallX, P. Levy and M. Frechet, among others (see the preface to Levy[2]). Nevertheless, the most fruitful direction in this field is the infinite dimensional integration theory initiated by N. Wiener and A. N. Kolmogorov which is closely related to the developments of the theory of stochastic processes. It was Wiener who constructed for the first time in 1923 a probability measure on the space of all continuous functions (i. e. the Wiener measure) which provided an ideal math ematical model for Brownian motion. Then some important properties of Wiener integrals, especially the quasi-invariance of Gaussian measures, were discovered by R. Cameron and W. Martin[l, 2, 3]. In 1931, Kolmogorov[l] deduced a second partial differential equation for transition probabilities of Markov processes order with continuous trajectories (i. e. diffusion processes) and thus revealed the deep connection between theories of differential equations and stochastic processes. The stochastic analysis created by K. Ito (also independently by Gihman [1]) in the forties is essentially an infinitesimal analysis for trajectories of stochastic processes. By virtue of Ito's stochastic differential equations one can construct diffusion processes via direct probabilistic methods and treat them as function als of Brownian paths (i. e. the Wiener functionals).

Infinite Dimensional Analysis

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Author : Charalambos D. Aliprantis
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-02

Infinite Dimensional Analysis written by Charalambos D. Aliprantis 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 2007-05-02 with Business & Economics categories.

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.

Tools For Infinite Dimensional Analysis

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Author : Jeremy J. Becnel
language : en
Publisher: CRC Press
Release Date : 2020-12-28

Tools For Infinite Dimensional Analysis written by Jeremy J. Becnel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-28 with Mathematics categories.

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

Interest Rate Models An Infinite Dimensional Stochastic Analysis Perspective

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Author : René Carmona
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-22

Interest Rate Models An Infinite Dimensional Stochastic Analysis Perspective written by René Carmona 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 2007-05-22 with Mathematics categories.

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

Functional Analysis And Infinite Dimensional Geometry

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Author : Marián J. Fabian
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-05-25

Functional Analysis And Infinite Dimensional Geometry written by Marián J. Fabian 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 2001-05-25 with Mathematics categories.

This book introduces the reader to the basic principles of functional analysis and to areas of Banach space theory that are close to nonlinear analysis and topology. In the first part, the book develops the classical theory, including weak topologies, locally convex spaces, Schauder bases, and compact operator theory. The presentation is self-contained, including many folklore results, and the proofs are accessible to students with the usual background in real analysis and topology. The second part covers topics in convexity and smoothness, finite representability, variational principles, homeomorphisms, weak compactness and more. Several results are published here for the first time in a monograph. The text can be used in graduate courses or for independent study. It includes a large number of exercises of different levels of difficulty, accompanied by hints. The book is also directed to young researchers in functional analysis and can serve as a reference book.This is an introduction to basic principles of functional analysis and to areas of Banach space theory close to nonlinear analysis and topology. The first part, which develops the classical theory, is self-contained and features a large number of exercises containing many important results. The second part covers selected topics in the theory of Banach spaces related to smoothness and topology. It is intended to be an introduction to and complement of existing books on the subject. This text may be used in graduate courses, for independent study, or as a reference book.

Infinite Dimensional Topology

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Author : J. van Mill
language : en
Publisher: Elsevier
Release Date : 1988-12-01

Infinite Dimensional Topology written by J. van Mill and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-12-01 with Mathematics categories.

The first part of this book is a text for graduate courses in topology. In chapters 1 - 5, part of the basic material of plane topology, combinatorial topology, dimension theory and ANR theory is presented. For a student who will go on in geometric or algebraic topology this material is a prerequisite for later work. Chapter 6 is an introduction to infinite-dimensional topology; it uses for the most part geometric methods, and gets to spectacular results fairly quickly. The second part of this book, chapters 7 & 8, is part of geometric topology and is meant for the more advanced mathematician interested in manifolds. The text is self-contained for readers with a modest knowledge of general topology and linear algebra; the necessary background material is collected in chapter 1, or developed as needed.One can look upon this book as a complete and self-contained proof of Toruńczyk's Hilbert cube manifold characterization theorem: a compact ANR X is a manifold modeled on the Hilbert cube if and only if X satisfies the disjoint-cells property. In the process of proving this result several interesting and useful detours are made.

An Introduction To Infinite Dimensional Linear Systems Theory

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Author : Ruth F. Curtain
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

An Introduction To Infinite Dimensional Linear Systems Theory written by Ruth F. Curtain 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 2012-12-06 with Mathematics categories.

Infinite dimensional systems is now an established area of research. Given the recent trend in systems theory and in applications towards a synthesis of time- and frequency-domain methods, there is a need for an introductory text which treats both state-space and frequency-domain aspects in an integrated fashion. The authors' primary aim is to write an introductory textbook for a course on infinite dimensional linear systems. An important consideration by the authors is that their book should be accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Consequently, all the mathematical background is summarized in an extensive appendix. For the majority of students, this would be their only acquaintance with infinite dimensional systems.

Infinite Dimensional Analysis Operators In Hilbert Space Stochastic Calculus Via Representations And Duality Theory

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Author : Palle Jorgensen
language : en
Publisher: World Scientific
Release Date : 2021-01-15

Infinite Dimensional Analysis Operators In Hilbert Space Stochastic Calculus Via Representations And Duality Theory written by Palle Jorgensen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-15 with Mathematics categories.

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.