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Author:   Oleg Klesov
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of the original 1st ed. 2014
Volume:   71
Dimensions:   Width: 15.50cm , Height: 2.60cm , Length: 23.50cm
Weight:   7.548kg
ISBN:  

9783662511503

ISBN 10:   3662511509
Pages:   483
Publication Date:   23 August 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

1.Notation and auxiliary results.- 2.Maximal inequalities for multiple sums.- 3.Weak convergence of multiple sums.- 4.Weak law of large numbers for multiple sums.- 5.Almost sure convergence for multiple series.- 6.Boundedness of multiple series.- 7.Rate of convergence of multiple sums.- 8.Strong law of large numbers for independent non-identically distributed random variables.- 9.Strong law of large numbers for independent identically distributed random variables.- 10.Law of the iterated logarithm.- 11.Renewal theorem for random walks with multidimensional time.- 12.Existence of moments of the supremum of multiple sums and the strong law of large numbers.- 13.Complete convergence.

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)

Author Information

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.

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