Limit Theorems for Multi-Indexed Sums of Random Variables
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Beschreibung
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.
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.
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
Autor*in
Oleg Klesov
Themen in »Limit Theorems for Multi-Indexed Sums of Random Variables«
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
Stimmen zu »Limit Theorems for Multi-Indexed Sums of Random Variables«
“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)
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