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141103  eng 
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a 9783662443880

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1 

a Klesov, Oleg

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0 
0 
a Limit Theorems for MultiIndexed Sums of Random Variables
h Elektronische Ressource
c by Oleg Klesov

250 


a 1st ed. 2014

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a Berlin, Heidelberg
b Springer Berlin Heidelberg
c 2014, 2014

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a XVIII, 483 p. 2 illus
b online resource

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0 

a 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 nonidentically 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

653 


a Statistical Theory and Methods

653 


a Statistics

653 


a Probability Theory

653 


a Mathematical physics

653 


a Mathematical Methods in Physics

653 


a Probabilities

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0 
7 
a eng
2 ISO 6392

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b Springer
a Springer eBooks 2005

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0 

a Probability Theory and Stochastic Modelling

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5 
0 
a 10.1007/9783662443880

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u https://doi.org/10.1007/9783662443880?nosfx=y
x Verlag
3 Volltext

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0 

a 519.2

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a 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 HajekRenyi 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
