Limit Theorems for Multi-Indexed Sums of Random Variables
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
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Oleg Klesov
Limit Theorems for Multi-Indexed Sums of Random Variables
Probability Theory and Stochastic Modelling Volume 71
Editors-in-Chief Søren Asmussen, Aarhus, Denmark Peter W. Glynn, Stanford, CA, USA Thomas G. Kurtz, Madison, WI, USA Yves Le Jan, Orsay, France Advisory Board Joe Gani, Canberra, ACT, Australia Martin Hairer, Coventry, UK Peter Jagers, Gothenburg, Sweden Ioannis Karatzas, New York, NY, USA Frank P. Kelly, Cambridge, UK Andreas E. Kyprianou, Bath, UK Bernt Øksendal, Oslo, Norway George Papanicolaou, Stanford, CA, USA Etienne Pardoux, Marseille, France Edwin Perkins, Vancouver, BC, Canada Halil Mete Soner, Zürich, Switzerland
The Stochastic Modelling and Probability Theory series is a merger and continuation of Springer’s two well established series Stochastic Modelling and Applied Probability and Probability and Its Applications series. It publishes research monographs that make a significant contribution to probability theory or an applications domain in which advanced probability methods are fundamental. Books in this series are expected to follow rigorous mathematical standards, while also displaying the expository quality necessary to make them useful and accessible to advanced students as well as researchers. The series covers all aspects of modern probability theory including • • • • • •
Gaussian processes Markov processes Random Fields, point processes and random sets Random matrices Statistical mechanics and random media Stochastic analysis
as well as applications that include (but are not restricted to): • Branching processes and other models of population growth • Communications and processing networks • Computational methods in probability and stochastic processes, includingsimulation • Genetics and other stochastic models in biology and the life sciences • Information theory, signal processing, and image synthesis • Mathematical economics and finance • Statistical methods (e.g. empirical processes, MCMC) • Statistics for stochastic processes • Stochastic control • Stochastic models in operations research and stochastic optimization • Stochastic models in the physical sciences More information about this series at http://www.springer.com/series/13205
Oleg Klesov
Limit Theorems for Multi-Indexed Sums of Random Variables
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Oleg Klesov Department of Mathematical Analysis and Probability Theory National Technical University of Ukraine “Kiev Polytechnic Institute” Kyiv Ukraine
ISSN 2199-3130 ISBN 978-3-662-44387-3 DOI 10.1007/978-3-662-44388-0
ISSN 2199-3149 (electronic) ISBN 978-3-662-44388-0 (eBook)
Library of Congress Control Number: 2014945956 Mathematics Subject Classification (2010): 60F15, 60F05, 60F10, 60E15, 60E07, 60E10, 60F20 Springer Heidelberg New York Dordrecht London © Springer-Verlag Berlin Heidelberg 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on mic
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