Real and stochastic analysis : current trends / edited by M. M. Rao, University of California at Riverside, USA.

Format:

Book

Contributor:

Rao, M. M. (Malempati Madhusudana), 1929- editor.

Series:

Gale eBooks

Standardized Title:

Real and stochastic analysis (World Scientific (Firm))

Language:

English

Subjects (All):

Stochastic analysis.

Physical Description:

1 online resource (xiv, 561 pages) : illustrations

Place of Publication:

New Jersey : World Scientific, [2014]

Language Note:

English

Summary:

This book presents the current status and research trends in Stochastic Analysis. Several new and emerging research areas are described in detail, highlighting the present outlook in Stochastic Analysis and its impact on abstract analysis. The book focuses on treating problems in areas that serve as a launching pad for continual research.

Contents:

CONTENTS; Preface; Introduction and Overview; References; 1. Gaussian Measures on Infinite-Dimensional Spaces; 0 Introduction; 0.1 Notation and terminology; 1 Gaussian Measures on Rd; 2 Infinite-Dimensional Gaussian Distributions; 3 The Wiener Measure; 4 Radon Gaussian Measures; 5 The Cameron-Martin Space and Measurable Linear Operators; 6 Zero-one Laws and Dichotomies; 7 The Ornstein-Uhlenbeck Semigroup; 8 The Hermite-Chebyshev Polynomials; 9 Sobolev Classes over Gaussian Measures; 10 Transformations of Gaussian Measures; 11 Convexity; 12 Open Problems; References

2. Random Fields and Hypergroups0 Introduction; 1 Commutative Hypergroups; 1.1 Definition and first examples; 1.1.1. Definition; 1.1.2. Example; 1.1.3. Example; 1.2 Some harmonic analysis; 1.2.1. Definition; 1.2.2. Definition; 1.2.3. Definition; 1.2.4. Back to the examples; 1.2.5. Definition; 1.2.6. Properties of the set PD(K); 1.2.7. Definition; 1.2.8. Properties of χ0-modifications; 1.3 Basic constructions of hypergroups; 1.3.1. Discrete polynomial hypergroups; 1.3.2. Compact polynomial hypergroups; 1.3.3. Sturm-Liouville hypergroups; 1.3.4. Higher rank Bessel hypergroups

2 Random Fields over Hypergroups2.1 Second order random fields; 2.1.1. Definition; 2.1.2. Definition; 2.1.3. Consequences; 2.1.4. Examples of stationary random fields over K; 2.1.5. Stationary random fields occurring in statistics; 2.2 Translation and decomposition; 2.2.1. Oscillations over K; 2.2.2. Proposition; 2.2.3.; 2.2.4. Proposition; 2.2.5. Orthogonal decompositions of random fields; 2.2.6. Examples; 2.2.7. Returning to moving averages; 2.3 Harmonizability; 2.3.1. Definition; 2.3.2. Theorem; 2.3.3. Corollary; 2.3.4. Definition; 2.3.5. Theorem; 2.3.6. Definition; 2.3.7.; 2.3.8. Theorem

2.3.9. Corollary2.3.10. Theorem; 2.3.11. Generation of harmonizable random fields; 3 Generalized Random Fields over Hypergroups; 3.1 Segal algebras; 3.1.1.; 3.1.2. Obvious facts; 3.1.3. Examples of Segal algebras; 3.1.4. Definition; 3.1.5.; 3.1.6. Definition; 3.1.7. Theorem; 3.1.8. Comments on the Proof of Theorem 3.1.7; 3.2 The extended Feichtinger algebra; 3.2.1. Definition; 3.2.2.; 3.2.3. Supplements on Segal algebras; 3.2.4. Definition; 3.2.5. Definition; 3.2.6. Examples of admissible hypergroups; 3.2.7. Definition; 3.2.8. Properties of the set SF (K); 3.2.9. Theorem; 3.2.10. Corollary

3.2.11. Theorem3.2.12. Lemma; 3.2.13. Theorem; 3.3 Covariance and duality; 3.3.1. Definition; 3.3.2. Lemma; 3.3.3. Notation; 3.3.4. Theorem; 3.3.5. Theorem; 3.3.6. Resume; 3.3.7. Definition; 3.3.8. Definition; 3.3.9. Properties of dualization; 3.3.10. Definition; 3.3.11. Properties of filtering; 3.3.12. Theorem; 3.3.13. Theorem; 3.3.14. Definition; 3.3.15. Theorem; 3.3.16. Discussion; 3.3.17. Definition; 3.3.18. Theorem; 3.3.19.; 3.4 Suggestions for further research; Bibliographical Notes; References; 3. A Concise Exposition of Large Deviations; 0 Introduction; 1 Definitions and Generalities

2 The Cramer Theorem

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

9789814551281

9814551287

OCLC:

869281894