Lectures on Gaussian Processes

• Main Author: Lifshits, Mikhail (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2012.
• Series: SpringerBriefs in Mathematics,
• Subjects: Mathematics.; Probabilities.; Probability Theory and Stochastic Processes.

Gaussian processes can be viewed as a  far-reaching infinite-dimensional extension of classical normal random variables. Their theory presents a powerful range of tools for probabilistic modelling in various academic and technical domains such as Statistics, Forecasting, Finance, Information Transmi...

Table of Contents:

• Preface
• 1.Gaussian Vectors and Distributions
• 2.Examples of Gaussian Vectors, Processes and Distributions
• 3.Gaussian White Noise and Integral Representations
• 4.Measurable Functionals and the Kernel
• 5.Cameron-Martin Theorem
• 6.Isoperimetric Inequality
• 7.Measure Concavity and Other Inequalities
• 8.Large Deviation Principle
• 9.Functional Law of the Iterated Logarithm
• 10.Metric Entropy and Sample Path Properties
• 11.Small Deviations
• 12.Expansions of Gaussian Vectors
• 13.Quantization of Gaussian Vectors
• 14.Invitation to Further Reading
• References.