Probability Theory and Stochastic Modelling

Limit Theorems for Multi-Indexed Sums of Random Variables

Authors: Klesov, Oleg

  • First unified treatment of the subject of limit theorems for multiple sums of independent random variables
  • Presents new results even for the classical setting
  • Offers a modern approach
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About this book

Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes.

Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals.

The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who work on limit theorems in probability theory, the statistical analysis of random fields, as well as in the field of random sets or stochastic geometry. The central topic is also important for statistical theory, developing statistical inferences for random fields, and also has applications to the sciences, including physics and chemistry.

About the authors

Oleg Klesov graduated from Kiev Shevchenko University in 1977 and obtained his PhD in 1979, followed by his habilitation in 2001. He is currently Professor at the National Technical University of Ukraine “Kyiv Polytechnic Institute”. During his academic career, he has held several positions as Invited Professor at Lublin (Poland), Debrecen (Hungary), Marburg, Koeln, Paderborn (Germany), Gainesville (USA), Cergy Pontoise (France), and Lakehead (Canada). His main scientific interests are in probability theory, stochastic processes and real analysis.

Reviews

“The book is well written and mathematically rigorous. … To date there is no book like the present one. All of the important results on multiple sums are scattered throughout the literature. … In summary, this is a useful book for a researcher in probability theory and mathematical statistics. It is very carefully written and collects results which are not easy to find in the literature or which had been even forgotten.” (Nikolai N. Leonenko, zbMATH 1318.60005, 2015)


Table of contents (13 chapters)

  • Some Remarks on the Theory of Limit Theorems for Multi-Indexed Sums

    Klesov, Oleg

    Pages 1-15

  • Maximal Inequalities for Multi-Indexed Sums of Independent Random Variables

    Klesov, Oleg

    Pages 17-47

  • Weak Convergence of Multi-Indexed Sums of Independent Random Variables

    Klesov, Oleg

    Pages 49-76

  • The Law of Large Numbers for Multi-Indexed Sums of Independent Random Variables

    Klesov, Oleg

    Pages 77-99

  • Almost Sure Convergence of Multi-Indexed Series

    Klesov, Oleg

    Pages 101-130

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-662-44388-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-662-44387-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-3-662-51150-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Limit Theorems for Multi-Indexed Sums of Random Variables
Authors
Series Title
Probability Theory and Stochastic Modelling
Series Volume
71
Copyright
2014
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-44388-0
DOI
10.1007/978-3-662-44388-0
Hardcover ISBN
978-3-662-44387-3
Softcover ISBN
978-3-662-51150-3
Series ISSN
2199-3130
Edition Number
1
Number of Pages
XVIII, 483
Number of Illustrations and Tables
2 b/w illustrations
Topics