Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Probability Theory and Stochastic Modelling (PTSM, volume 71)
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Table of contents (13 chapters)
Keywords
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.
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)
Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: Limit Theorems for Multi-Indexed Sums of Random Variables
Authors: Oleg Klesov
Series Title: Probability Theory and Stochastic Modelling
DOI: https://doi.org/10.1007/978-3-662-44388-0
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2014
Hardcover ISBN: 978-3-662-44387-3Published: 24 October 2014
Softcover ISBN: 978-3-662-51150-3Published: 23 August 2016
eBook ISBN: 978-3-662-44388-0Published: 13 October 2014
Series ISSN: 2199-3130
Series E-ISSN: 2199-3149
Edition Number: 1
Number of Pages: XVIII, 483
Number of Illustrations: 2 b/w illustrations
Topics: Probability Theory and Stochastic Processes, Statistical Theory and Methods, Mathematical Methods in Physics