Young measures on topological spaces :with applications in control theory and probability theory
- 作者: Castaing, Charles,
- 其他作者: Raynaud de Fitte, Paul, , Valadier, Michel,
- 出版: Dordrecht ;Boston : Kluwer Academic Publishers ©2004.
- 稽核項: 1 online resource (xi, 320 pages).
- 叢書名: Mathematics and its applications ;v. 571
- 標題: Topology. , Topological spaces. , MATHEMATICS Topology. , Electronic books. , Espaces topologiques. , MATHEMATICS
- ISBN: 1402019637 , 9781402019630
- ISBN: 1402019637
- 試查全文@TNUA:
- 附註: Includes bibliographical references (pages 295-314) and indexes. Preface -- Generalities, Preliminary results -- Young Measures, the four Stable Topologies: S, M, N, W -- Convergence in Probability of Young Measures (with some applications to stable convergence) -- Compactness -- Strong Tightness -- Young Measures on Banach Spaces. Application -- Applications in Control Theory -- Semicontinuity of Integral Functionals using Young Measures -- Stable Convergence in Limit Theorems of Probability Theory.
- 摘要: 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).
- 電子資源: https://dbs.tnua.edu.tw/login?url=https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=118529
- 系統號: 005312155
- 資料類型: 電子書
- 讀者標籤: 需登入
- 引用網址: 複製連結
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).
來源: Google Book
來源: Google Book
評分
