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Mikhail Lifshits

Lectures on Gaussian Processes


2012. 2012. x, 121 S. X, 121p. 235 mm
Verlag/Jahr: SPRINGER, BERLIN 2012
ISBN: 3-642-24938-8 (3642249388)
Neue ISBN: 978-3-642-24938-9 (9783642249389)

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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.
From the reviews:
"This is a book on the modern theory of Gaussian processes. ... I would like to recommend this book to anyone interested in the most recent developments regarding Gaussian processes and wanting to learn them from one of the best specialists in the field." (Ivan Nourdin, Mathematical Reviews, December, 2013)