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This volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics.The topics presented in this volume are:This book is intended not only for graduate students in mathematics or physics, but also for mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.
Book Synopsis Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics by : Wilfried Grecksch
Download or read book Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics written by Wilfried Grecksch and published by World Scientific. This book was released on 2020-04-22 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics.The topics presented in this volume are:This book is intended not only for graduate students in mathematics or physics, but also for mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.
Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability. While the theory of such equations is well establ
Book Synopsis Stability of Infinite Dimensional Stochastic Differential Equations with Applications by : Kai Liu
Download or read book Stability of Infinite Dimensional Stochastic Differential Equations with Applications written by Kai Liu and published by CRC Press. This book was released on 2005-08-23 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability. While the theory of such equations is well establ
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 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
Updates in this second edition include two brand new chapters and an even more comprehensive bibliography.
Book Synopsis Stochastic Equations in Infinite Dimensions by : Giuseppe Da Prato
Download or read book Stochastic Equations in Infinite Dimensions written by Giuseppe Da Prato and published by Cambridge University Press. This book was released on 2014-04-17 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Updates in this second edition include two brand new chapters and an even more comprehensive bibliography.
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 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.
Kolmogorov equations are second order parabolic equations with a finite or an infinite number of variables. They are deeply connected with stochastic differential equations in finite or infinite dimensional spaces. They arise in many fields as Mathematical Physics, Chemistry and Mathematical Finance. These equations can be studied both by probabilistic and by analytic methods, using such tools as Gaussian measures, Dirichlet Forms, and stochastic calculus. The following courses have been delivered: N.V. Krylov presented Kolmogorov equations coming from finite-dimensional equations, giving existence, uniqueness and regularity results. M. Röckner has presented an approach to Kolmogorov equations in infinite dimensions, based on an LP-analysis of the corresponding diffusion operators with respect to suitably chosen measures. J. Zabczyk started from classical results of L. Gross, on the heat equation in infinite dimension, and discussed some recent results.
Book Synopsis Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions by : N.V. Krylov
Download or read book Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions written by N.V. Krylov and published by Springer. This book was released on 2006-11-15 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kolmogorov equations are second order parabolic equations with a finite or an infinite number of variables. They are deeply connected with stochastic differential equations in finite or infinite dimensional spaces. They arise in many fields as Mathematical Physics, Chemistry and Mathematical Finance. These equations can be studied both by probabilistic and by analytic methods, using such tools as Gaussian measures, Dirichlet Forms, and stochastic calculus. The following courses have been delivered: N.V. Krylov presented Kolmogorov equations coming from finite-dimensional equations, giving existence, uniqueness and regularity results. M. Röckner has presented an approach to Kolmogorov equations in infinite dimensions, based on an LP-analysis of the corresponding diffusion operators with respect to suitably chosen measures. J. Zabczyk started from classical results of L. Gross, on the heat equation in infinite dimension, and discussed some recent results.
Book Synopsis Stochastic Equations in Infinite Dimensions, Second Edition by : Giuseppe Da Prato
Download or read book Stochastic Equations in Infinite Dimensions, Second Edition written by Giuseppe Da Prato and published by . This book was released on 2014 with total page 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 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.
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.)
Book Synopsis Stochastic Analysis on Infinite Dimensional Spaces by : H Kunita
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.)
The last few years have seen a number of major developments demonstrating that the long-term behavior of solutions of a very large class of partial differential equations possesses a striking resemblance to the behavior of solutions of finite dimensional dynamical systems, or ordinary differential equations. The first of these advances was the discovery that a dissipative PDE has a compact, global attractor with finite Hausdorff and fractal dimensions. More recently, it was shown that some of these PDEs possess a finite dimensional inertial manifold-that is, an invariant manifold containing the attractor and exponentially attractive trajectories. With the improved understanding of the exact connection between finite dimensional dynamical systems and various classes of dissipative PDEs, it is now realistic to hope that the wealth of studies of such topics as bifurcations of finite vector fields and ``strange'' fractal attractors can be brought to bear on various mathematical models, including continuum flows. Surprisingly, a number of distributed systems from continuum mechanics have been found to exhibit the same nontrivial dynamic behavior as observed in low-dimensional dynamical systems. As a natural consequence of these observations, a new direction of research has arisen: detection and analysis of finite dimensional dynamical characteristics of infinite-dimensional systems. This book represents the proceedings of an AMS-IMS-SIAM Summer Research Conference, held in July, 1987 at the University of Colorado at Boulder. Bringing together mathematicians and physicists, the conference provided a forum for presentations on the latest developments in the field and fostered lively interactions on open questions and future directions. With contributions from some of the top experts, these proceedings will provide readers with an overview of this vital area of research.
Book Synopsis The Connection between Infinite Dimensional and Finite Dimensional Dynamical Systems by : Basil Nicolaenko
Download or read book The Connection between Infinite Dimensional and Finite Dimensional Dynamical Systems written by Basil Nicolaenko and published by American Mathematical Soc.. This book was released on 1989 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last few years have seen a number of major developments demonstrating that the long-term behavior of solutions of a very large class of partial differential equations possesses a striking resemblance to the behavior of solutions of finite dimensional dynamical systems, or ordinary differential equations. The first of these advances was the discovery that a dissipative PDE has a compact, global attractor with finite Hausdorff and fractal dimensions. More recently, it was shown that some of these PDEs possess a finite dimensional inertial manifold-that is, an invariant manifold containing the attractor and exponentially attractive trajectories. With the improved understanding of the exact connection between finite dimensional dynamical systems and various classes of dissipative PDEs, it is now realistic to hope that the wealth of studies of such topics as bifurcations of finite vector fields and ``strange'' fractal attractors can be brought to bear on various mathematical models, including continuum flows. Surprisingly, a number of distributed systems from continuum mechanics have been found to exhibit the same nontrivial dynamic behavior as observed in low-dimensional dynamical systems. As a natural consequence of these observations, a new direction of research has arisen: detection and analysis of finite dimensional dynamical characteristics of infinite-dimensional systems. This book represents the proceedings of an AMS-IMS-SIAM Summer Research Conference, held in July, 1987 at the University of Colorado at Boulder. Bringing together mathematicians and physicists, the conference provided a forum for presentations on the latest developments in the field and fostered lively interactions on open questions and future directions. With contributions from some of the top experts, these proceedings will provide readers with an overview of this vital area of research.
