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

Author : Palle Jorgensen,James Tian
Publisher : World Scientific
Page : 253 pages
File Size : 47,6 Mb
Release : 2021-01-15
Category : Mathematics
ISBN : 9789811225796

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Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory by Palle Jorgensen,James Tian Pdf

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.

Author : Palle E. T. Jørgensen,James F. Tian
Publisher : Unknown
Page : 253 pages
File Size : 43,9 Mb
Release : 2021
Category : Electronic books
ISBN : 9811225788

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Infinite-dimensional Analysis by Palle E. T. Jørgensen,James F. Tian Pdf

Author : H Kunita,Hui-Hsiung Kuo
Publisher : CRC Press
Page : 340 pages
File Size : 42,8 Mb
Release : 1994-08-22
Category : Mathematics
ISBN : 0582244900

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Stochastic Analysis on Infinite Dimensional Spaces by H Kunita,Hui-Hsiung Kuo Pdf

The book discusses the following topics in stochastic analysis: 1. Stochastic analysis related to Lie groups: stochastic analysis of loop spaces and infinite dimensional manifolds has been developed rapidly after the fundamental works of Gross and Malliavin. (Lectures by Driver, Gross, Mitoma, and Sengupta.)

Author : Tijana Levajković,Hermann Mena
Publisher : Springer
Page : 132 pages
File Size : 42,6 Mb
Release : 2017-08-31
Category : Mathematics
ISBN : 9783319656786

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Equations Involving Malliavin Calculus Operators by Tijana Levajković,Hermann Mena Pdf

This book provides a comprehensive and unified introduction to stochastic differential equations and related optimal control problems. The material is new and the presentation is reader-friendly. A major contribution of the book is the development of generalized Malliavin calculus in the framework of white noise analysis, based on chaos expansion representation of stochastic processes and its application for solving several classes of stochastic differential equations with singular data involving the main operators of Malliavin calculus. In addition, applications in optimal control and numerical approximations are discussed. The book is divided into four chapters. The first, entitled White Noise Analysis and Chaos Expansions, includes notation and provides the reader with the theoretical background needed to understand the subsequent chapters. In Chapter 2, Generalized Operators of Malliavin Calculus, the Malliavin derivative operator, the Skorokhod integral and the Ornstein-Uhlenbeck operator are introduced in terms of chaos expansions. The main properties of the operators, which are known in the literature for the square integrable processes, are proven using the chaos expansion approach and extended for generalized and test stochastic processes. Chapter 3, Equations involving Malliavin Calculus operators, is devoted to the study of several types of stochastic differential equations that involve the operators of Malliavin calculus, introduced in the previous chapter. Fractional versions of these operators are also discussed. Finally, in Chapter 4, Applications and Numerical Approximations are discussed. Specifically, we consider the stochastic linear quadratic optimal control problem with different forms of noise disturbances, operator differential algebraic equations arising in fluid dynamics, stationary equations and fractional versions of the equations studied – applications never covered in the extant literature. Moreover, numerical validations of the method are provided for specific problems."

Author : Giuseppe Da Prato,Luciano Tubaro
Publisher : Springer
Page : 265 pages
File Size : 51,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540474081

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Stochastic Partial Differential Equations and Applications by Giuseppe Da Prato,Luciano Tubaro Pdf

Author : Giuseppe Da Prato
Publisher : Springer Science & Business Media
Page : 208 pages
File Size : 48,7 Mb
Release : 2006-08-25
Category : Mathematics
ISBN : 9783540290216

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An Introduction to Infinite-Dimensional Analysis by Giuseppe Da Prato Pdf

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.

Author : Zhi-yuan Huang,Jia-An Yan
Publisher : Kluwer Academic Publishers
Page : 296 pages
File Size : 45,5 Mb
Release : 2000
Category : Function spaces
ISBN : 7030078187

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Introduction to Infinite Dimensional Stochastic Analysis by Zhi-yuan Huang,Jia-An Yan Pdf

This book offers a concise introduction to the rapidly expanding field of infinite dimensional stochastic analysis. It treats Malliavin calculus and white noise analysis in a single book, presenting these two different areas in a unified setting of Gaussian probability spaces. Topics include recent results and developments in the areas of quasi-sure analysis, anticipating stochastic calculus, generalised operator theory and applications in quantum physics. A short overview on the foundations of infinite dimensional analysis is given. Audience: This volume will be of interest to researchers and graduate students whose work involves probability theory, stochastic processes, functional analysis, operator theory, mathematics of physics and abstract harmonic analysis.

Author : Marshall Harvey Stone
Publisher : American Mathematical Soc.
Page : 632 pages
File Size : 45,6 Mb
Release : 1932-12-31
Category : Mathematics
ISBN : 9780821810156

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Linear Transformations in Hilbert Space and Their Applications to Analysis by Marshall Harvey Stone Pdf

Author : UNESCO
Publisher : UNESCO Publishing
Page : 991 pages
File Size : 52,9 Mb
Release : 2008-12-31
Category : Political Science
ISBN : 9789231040832

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History of Humanity by UNESCO Pdf

This is the seventh and final volume in this comprehensive guide to the history of world cultures throughout historical times.

Author : Jorgensen Palle,Tian Feng
Publisher : World Scientific
Page : 564 pages
File Size : 41,7 Mb
Release : 2017-01-24
Category : Mathematics
ISBN : 9789813202146

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Non-commutative Analysis by Jorgensen Palle,Tian Feng Pdf

The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret "non-commutative analysis" broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.) A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras. The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.

Author : Giorgio Fabbri,Fausto Gozzi,Andrzej Święch
Publisher : Springer
Page : 916 pages
File Size : 46,9 Mb
Release : 2017-06-22
Category : Mathematics
ISBN : 9783319530673

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Stochastic Optimal Control in Infinite Dimension by Giorgio Fabbri,Fausto Gozzi,Andrzej Święch Pdf

Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite dimension. Readers from other fields who want to learn the basic theory will also find it useful. The prerequisites are: standard functional analysis, the theory of semigroups of operators and its use in the study of PDEs, some knowledge of the dynamic programming approach to stochastic optimal control problems in finite dimension, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.

Author : David Applebaum,B.V. Rajarama Bhat,Johan Kustermans,J. Martin Lindsay
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 48,7 Mb
Release : 2005-02-18
Category : Mathematics
ISBN : 3540244069

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Quantum Independent Increment Processes I by David Applebaum,B.V. Rajarama Bhat,Johan Kustermans,J. Martin Lindsay Pdf

This volume is the first of two volumes containing the revised and completed notes lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald during the period March 9 – 22, 2003, and supported by the Volkswagen Foundation. The school gave an introduction to current research on quantum independent increment processes aimed at graduate students and non-specialists working in classical and quantum probability, operator algebras, and mathematical physics. The present first volume contains the following lectures: "Lévy Processes in Euclidean Spaces and Groups" by David Applebaum, "Locally Compact Quantum Groups" by Johan Kustermans, "Quantum Stochastic Analysis" by J. Martin Lindsay, and "Dilations, Cocycles and Product Systems" by B.V. Rajarama Bhat.

Author : Haim Brezis
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 44,5 Mb
Release : 2010-11-02
Category : Mathematics
ISBN : 9780387709147

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Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis Pdf

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.

Author : Anonim
Publisher : Unknown
Page : 684 pages
File Size : 45,6 Mb
Release : 1989
Category : Functional analysis
ISBN : UCAL:B4342788

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Reviews in Functional Analysis, 1980-86 by Anonim Pdf

These four volumes contain the almost 12,000 reviews appearing in Mathematical Reviews under primary or secondary subject classification 46, Functional Analysis, between 1980 and 1986.

Author : Ola Bratteli,Palle E. T. Jørgensen
Publisher : American Mathematical Soc.
Page : 106 pages
File Size : 51,8 Mb
Release : 1999
Category : C*-algebras
ISBN : 9780821809624

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Iterated Function Systems and Permutation Representations of the Cuntz Algebra by Ola Bratteli,Palle E. T. Jørgensen Pdf

This book is intended for graduate students and research mathematicians working in functional analysis.