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

Author : Palle Jorgensen
Publisher : World Scientific
ISBN 13 : 9811225796
Total Pages : 253 pages
Book Rating : 4.96/5 ( download)

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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.

Author : Palle E. T. Jørgensen
Publisher :
ISBN 13 : 9789811225789
Total Pages : 253 pages
Book Rating : 4.88/5 ( download)

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Download or read book Infinite-dimensional Analysis written by Palle E. T. Jørgensen and published by . This book was released on 2021 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : H Kunita
Publisher : CRC Press
ISBN 13 : 9780582244900
Total Pages : 340 pages
Book Rating : 4.00/5 ( download)

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Download or read book Stochastic Analysis on Infinite Dimensional Spaces written by H Kunita and published by CRC Press. This book was released on 1994-08-22 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : Springer
ISBN 13 : 3319656783
Total Pages : 132 pages
Book Rating : 4.86/5 ( download)

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Download or read book Equations Involving Malliavin Calculus Operators written by Tijana Levajković and published by Springer. This book was released on 2017-08-31 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : Springer
ISBN 13 : 3540474080
Total Pages : 265 pages
Book Rating : 4.81/5 ( download)

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Download or read book Stochastic Partial Differential Equations and Applications written by Giuseppe Da Prato and published by Springer. This book was released on 2006-11-15 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Giuseppe Da Prato
Publisher : Springer Science & Business Media
ISBN 13 : 3540290214
Total Pages : 217 pages
Book Rating : 4.16/5 ( download)

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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.

Author : Giorgio Fabbri
Publisher : Springer
ISBN 13 : 3319530674
Total Pages : 916 pages
Book Rating : 4.73/5 ( download)

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Download or read book Stochastic Optimal Control in Infinite Dimension written by Giorgio Fabbri and published by Springer. This book was released on 2017-06-22 with total page 916 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Marshall Harvey Stone
Publisher : American Mathematical Soc.
ISBN 13 : 0821810154
Total Pages : 632 pages
Book Rating : 4.56/5 ( download)

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Download or read book Linear Transformations in Hilbert Space and Their Applications to Analysis written by Marshall Harvey Stone and published by American Mathematical Soc.. This book was released on 1932-12-31 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Zhi-yuan Huang
Publisher : Kluwer Academic Publishers
ISBN 13 : 9787030078186
Total Pages : 296 pages
Book Rating : 4.87/5 ( download)

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Download or read book Introduction to Infinite Dimensional Stochastic Analysis written by Zhi-yuan Huang and published by Kluwer Academic Publishers. This book was released on 2000 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Jorgensen Palle
Publisher : World Scientific
ISBN 13 : 9813202149
Total Pages : 564 pages
Book Rating : 4.46/5 ( download)

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Download or read book Non-commutative Analysis written by Jorgensen Palle and published by World Scientific. This book was released on 2017-01-24 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.