Invariant Random Fields on Spaces with a Group Action

1. Front Matter

   Pages I-XVII

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2. Introduction

   • Anatoliy Malyarenko

   Pages 1-8

3. Spectral Expansions

   • Anatoliy Malyarenko

   Pages 9-89

4. L ² Theory of Invariant Random Fields

   • Anatoliy Malyarenko

   Pages 91-113

5. Sample Path Properties of Gaussian Invariant Random Fields

   • Anatoliy Malyarenko

   Pages 115-169

6. Applications

   • Anatoliy Malyarenko

   Pages 171-201

7. Appendix A: Mathematical Background

   • Anatoliy Malyarenko

   Pages 203-255

8. Back Matter

   Pages 257-261

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The author describes the current state of the art in the theory of invariant random fields. This theory is based on several different areas of mathematics, including probability theory, differential geometry, harmonic analysis, and special functions. The present volume unifies many results scattered throughout the mathematical, physical, and engineering literature, as well as it introduces new results from this area first proved by the author. The book also presents many practical applications, in particular in such highly interesting areas as approximation theory, cosmology and earthquake engineering. It is intended for researchers and specialists working in the fields of stochastic processes, statistics, functional analysis, astronomy, and engineering. 

• 60G60, 60G17, 60G22, 85A40
• cosmic microwave background
• limit theorems
• random field
• sample paths properties
• spectral expansion

From the reviews:

“This book is a nice addition to the list of very interesting books on random fields and their applications published in recent years. It focuses on invariant random fields on general spaces with a group action … and their applications. … This book is interesting to read and useful not only for researchers and graduate students in probability and statistics, but also for people who are interested in applications of random fields in various scientific areas.” (Yimin Xiao, Mathematical Reviews, March, 2014)

“The book is devoted to random fields possessing various invariance properties. … The book gives self-contained exposition of interesting and important problems arising in the theory of invariant random fields. … The book is useful for researchers, graduate and postgraduate students interested in the theory of random fields and their applications.” (Alexander V. Bulinski, zbMATH, Vol. 1268, 2013)

• School of Education, Culture, and Communication, Mälardalen University, Västerås, Sweden

  Anatoliy Malyarenko

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