Ebook: Probability in Banach Spaces: Isoperimetry and Processes
- Tags: Probability Theory and Stochastic Processes, Real Functions, Systems Theory Control, Calculus of Variations and Optimal Control, Optimization
- Series: Ergebnisse der Mathematik und ihrer Grenzgebiete 23
- Year: 1991
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.
Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.
Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.
Content:
Front Matter....Pages I-XII
Introduction....Pages 1-6
Notation....Pages 7-12
Front Matter....Pages 13-13
Isoperimetric Inequalities and the Concentration of Measure Phenomenon....Pages 14-36
Generalities on Banach Space Valued Random Variables and Random Processes....Pages 37-52
Front Matter....Pages 53-53
Gaussian Random Variables....Pages 54-88
Rademacher Averages....Pages 89-121
Stable Random Variables....Pages 122-148
Sums of Independent Random Variables....Pages 149-177
The Strong Law of Large Numbers....Pages 178-195
The Law of the Iterated Logarithm....Pages 196-234
Front Matter....Pages 235-235
Type and Cotype of Banach Spaces....Pages 236-271
The Central Limit Theorem....Pages 272-296
Regularity of Random Processes....Pages 297-331
Regularity of Gaussian and Stable Processes....Pages 332-364
Stationary Processes and Random Fourier Series....Pages 365-393
Empirical Process Methods in Probability in Banach Spaces....Pages 394-420
Applications to Banach Space Theory....Pages 421-460
Back Matter....Pages 461-482
Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.
Content:
Front Matter....Pages I-XII
Introduction....Pages 1-6
Notation....Pages 7-12
Front Matter....Pages 13-13
Isoperimetric Inequalities and the Concentration of Measure Phenomenon....Pages 14-36
Generalities on Banach Space Valued Random Variables and Random Processes....Pages 37-52
Front Matter....Pages 53-53
Gaussian Random Variables....Pages 54-88
Rademacher Averages....Pages 89-121
Stable Random Variables....Pages 122-148
Sums of Independent Random Variables....Pages 149-177
The Strong Law of Large Numbers....Pages 178-195
The Law of the Iterated Logarithm....Pages 196-234
Front Matter....Pages 235-235
Type and Cotype of Banach Spaces....Pages 236-271
The Central Limit Theorem....Pages 272-296
Regularity of Random Processes....Pages 297-331
Regularity of Gaussian and Stable Processes....Pages 332-364
Stationary Processes and Random Fourier Series....Pages 365-393
Empirical Process Methods in Probability in Banach Spaces....Pages 394-420
Applications to Banach Space Theory....Pages 421-460
Back Matter....Pages 461-482
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