Limit Theorems for Multi-Indexed Sums of Random Variables

  • Oleg┬áKlesov

Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 71)

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.


60F15, 60F05, 60F10, 60E15, 60E07, 60E10, 60F20 almost sure convergence law of the iterated logarithm limit theorems of probability theory multiple sums strong law of large numbers

Authors and affiliations

  • Oleg┬áKlesov
    • 1
  1. 1.Department of Mathematical Analysis, and Probability TheoryNational Technical University of Ukraine, Kiev Polytechnic InstituteKyivUkraine

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2014
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-662-44387-3
  • Online ISBN 978-3-662-44388-0
  • Series Print ISSN 2199-3130
  • Series Online ISSN 2199-3149
  • About this book