Sinossi
As in the case of the two previous volumes published in 1986 and 1997, the purpose of this monograph is to focus the interplay between real (functional) analysis and stochastic analysis show their mutual benefits and advance the subjects. The presentation of each article, given as a chapter, is in a research-expository style covering the respective topics in depth. In fact, most of the details are included so that each work is essentially self contained and thus will be of use both for advanced graduate students and other researchers interested in the areas considered. Moreover, numerous new problems for future research are suggested in each chapter. The presented articles contain a substantial number of new results as well as unified and simplified accounts of previously known ones. A large part of the material cov ered is on stochastic differential equations on various structures, together with some applications. Although Brownian motion plays a key role, (semi-) martingale theory is important for a considerable extent. Moreover, noncommutative analysis and probabil ity have a prominent role in some chapters, with new ideas and results. A more detailed outline of each of the articles appears in the introduction and outline to assist readers in selecting and starting their work. All chapters have been reviewed.
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Recensione
"Although most of the papers contain new results and/or proofs, their authors tried to make them reasonably self-contained and provide a wide background to the problems studied, so the papers should be accessible to advanced graduate students and serve as an introduction to some topics which have been paid considerable attention recently."
―Applications of Mathematics
Contenuti
* Preface * Rao: Introduction and Outline * Bell: Stochastic Differential Equations and Hypoelliptic Operators * Driver: Curved Wiener Space Analysis * Gudder: Noncommutative Probability and Applications * Jefferies: Advances and Applications of the Feynman Integral * Kunita: Stochastic Differential Equations Based on Levy Processes and Stochastic Flows of Diffeomorphisms * Rao: Convolutions of Vector Fields - II: Amenability and Spectral Properties * Index
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Gebundene Ausgabe. Condizione: Neu. Neu Neuware; new item; -The interplay between functional and stochastic analysis has wide implications for problems in partial differential equations, noncommutative or 'free' probability, and Riemannian geometry. Written by active researchers, each of the six independent chapters in this volume is devoted to a particular application of functional analytic methods in stochastic analysis, ranging from work in hypoelliptic operators to quantum field theory. Every chapter contains substantial new results as well as a clear, unified account of the existing theory; relevant references and numerous open problems are also included. Key topics: \* Stochastic differential equations (SDEs), hypoelliptic operators, and SDEs based on Lévy processes \* Stochastic calculus on Riemannian manifolds and curved Wiener spaces \* Noncommutative and quantum probability \* The Feynman integral, evolution processes, the FeynmanKac formula, and applications to quantum field theory \* Convolution operators and the amenability of the underlying locally compact groups, with connections among classical random walks, spectral theory, and Beurling and Segal subalgebras Self-contained, well-motivated, and replete with suggestions for further investigation, this book will be especially valuable as a seminar text for dissertation-level graduate students. Research mathematicians and physicists will also find it a useful and stimulating reference. Contributors: D.R. Bell; B.K. Driver; S. Gudder; B. Jefferies; H. Kunita; and M.M. Rao. 406 pp. Englisch. Codice articolo INF1000015237
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Gebundene Ausgabe. Condizione: Neu. Neu Neuware; new item; -The interplay between functional and stochastic analysis has wide implications for problems in partial differential equations, noncommutative or 'free' probability, and Riemannian geometry. Written by active researchers, each of the six independent chapters in this volume is devoted to a particular application of functional analytic methods in stochastic analysis, ranging from work in hypoelliptic operators to quantum field theory. Every chapter contains substantial new results as well as a clear, unified account of the existing theory; relevant references and numerous open problems are also included. Key topics: \* Stochastic differential equations (SDEs), hypoelliptic operators, and SDEs based on Lévy processes \* Stochastic calculus on Riemannian manifolds and curved Wiener spaces \* Noncommutative and quantum probability \* The Feynman integral, evolution processes, the FeynmanKac formula, and applications to quantum field theory \* Convolution operators and the amenability of the underlying locally compact groups, with connections among classical random walks, spectral theory, and Beurling and Segal subalgebras Self-contained, well-motivated, and replete with suggestions for further investigation, this book will be especially valuable as a seminar text for dissertation-level graduate students. Research mathematicians and physicists will also find it a useful and stimulating reference. Contributors: D.R. Bell; B.K. Driver; S. Gudder; B. Jefferies; H. Kunita; and M.M. Rao. 406 pp. Englisch. Codice articolo INF1000015237
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Real and Stochastic Analysis: New Perspectives (Trends in Mathematics)
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Birkhäuser Boston, 2004
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