This book is devoted to a systematic analysis of asymptotic behavior of distributions of various typical functionals of Gaussian random variables and fields. The text begins with an extended introduction, which explains fundamental ideas and sketches the basic methods fully presented later in the book. Good approximate formulas and sharp estimates of the remainders are obtained for a large class of Gaussian and similar processes. The author devotes special attention to the development of asymptotic analysis methods, emphasizing the method of comparison, the double-sum method and the method of moments. The author has added an extended introduction and has significantly revised the text for this translation, particularly the material on the double-sum method.

Readership

Graduate students and research mathematicians working in probability, mathematical statistics, and random processes.

Reviews

"a ... valuable addition to the set of English-language monographs dealing with related topics."

-- Mathematical Reviews

"[This] English edition is completed by a most welcome introduction. This book will be helpful to researchers and graduate students working in probability theory, mathematical statistics and random processes. It will provide them with the necessary tools for a thorough investigation of the asymptotic behavior of functionals of Gaussian processes and fields."

-- Metrika, International Journal for Theoretical and Applied Statistics

Table of Contents

• Introduction
• The method of comparison
• The double sum method
• The method of moments
• Limit theorems for the number of high excursions and for maxima of Gaussian processes and fields
• References