Paul Raynaud de Fitte's Books

Young Measures on Topological Spaces

With Applications in Control Theory and Probability Theory

By: Charles Castaing,Paul Raynaud de Fitte,Michel Valadier

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Young Measures on Topological Spaces

With Applications in Control Theory and Probability Theory

By: Charles Castaing,Paul Raynaud de Fitte,Michel Valadier

Young measures are now a widely used tool in the Calculus of Variations, in Control Theory, in Probability Theory and other fields. They are known under different names such as "relaxed controls," "fuzzy random variables" and many other names. This monograph provides a unified presentation of the theory, along with new results and applications in various fields. It can serve as a reference on the subject. Young measures are presented in a general setting which includes finite and for the first time infinite dimensional spaces: the fields of applications of Young measures (Control Theory, Calculus of Variations, Probability Theory...) are often concerned with problems in infinite dimensional settings. The theory of Young measures is now well understood in a finite dimensional setting, but open problems remain in the infinite dimensional case. We provide several new results in the general frame, which are new even in the finite dimensional setting, such as characterizations of convergence in measure of Young measures (Chapter 3) and compactness criteria (Chapter 4).These results are established under a different form (and with less details and developments) in recent papers by the same authors. We also provide new applications to Visintin and Reshetnyak type theorems (Chapters 6 and 8), existence of solutions to differential inclusions (Chapter 7), dynamical programming (Chapter 8) and the Central Limit Theorem in locally convex spaces (Chapter 9).

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Page Count

327

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1402019645

ISBN 13

9781402019647

Weak Dependence: With Examples and Applications

By: Jérome Dedecker,Paul Doukhan,Gabriel Lang,José Rafael Leon,Sana Louhichi,Clémentine Prieur

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Weak Dependence: With Examples and Applications

By: Jérome Dedecker,Paul Doukhan,Gabriel Lang,José Rafael Leon,Sana Louhichi,Clémentine Prieur

This book develops Doukhan/Louhichi's 1999 idea to measure asymptotic independence of a random process. The authors, who helped develop this theory, propose examples of models fitting such conditions: stable Markov chains, dynamical systems or more complicated models, nonlinear, non-Markovian, and heteroskedastic models with infinite memory. Applications are still needed to develop a method of analysis for nonlinear times series, and this book provides a strong basis for additional studies.

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Page Count

326

Publisher

Springer Science & Business Media

Published Date

ISBN 10

038769952X

ISBN 13

9780387699523

Young Measures on Topological Spaces

With Applications in Control Theory and Probability Theory

By: Charles Castaing,Paul Raynaud de Fitte,Michel Valadier

Write a review Read reviews Take a Quiz Solve Book Puzzle

Young Measures on Topological Spaces

With Applications in Control Theory and Probability Theory

By: Charles Castaing,Paul Raynaud de Fitte,Michel Valadier

Young measures are now a widely used tool in the Calculus of Variations, in Control Theory, in Probability Theory and other fields. They are known under different names such as "relaxed controls", "fuzzy random variables" and many other names. This monograph provides a unified presentation of the theory, along with new results and applications in various fields. It can serve as a reference on the subject. Young measures are presented in a general setting which includes finite and for the first time infinite dimensional spaces: the fields of applications of Young measures (Control Theory, Calculus of Variations, Probability Theory...) are often concerned with problems in infinite dimensional settings. The theory of Young measures is now well understood in a finite dimensional setting, but open problems remain in the infinite dimensional case. We provide several new results in the general frame, which are new even in the finite dimensional setting, such as characterizations of convergence in measure of Young measures (Chapter 3) and compactness criteria (Chapter 4).These results are established under a different form (and with fewer details and developments) in recent papers by the same authors. We also provide new applications to Visintin and Reshetnyak type theorems (Chapters 6 and 8), existence of solutions to differential inclusions (Chapter 7), dynamical programming (Chapter 8) and the Central Limit Theorem in locally convex spaces (Chapter 9).

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Solve jigsaw puzzle

Age

Page Count

327

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1402019637

ISBN 13

9781402019630

Book's by Paul Raynaud de Fitte

Young Measures on Topological Spaces

Young Measures on Topological Spaces

Weak Dependence: With Examples and Applications

Weak Dependence: With Examples and Applications

Young Measures on Topological Spaces

Young Measures on Topological Spaces

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