Coverart for item
The Resource Limit theorems for multi-indexed sums of random variables, Oleg Klesov

Limit theorems for multi-indexed sums of random variables, Oleg Klesov

Label
Limit theorems for multi-indexed sums of random variables
Title
Limit theorems for multi-indexed sums of random variables
Statement of responsibility
Oleg Klesov
Creator
Author
Subject
Language
eng
Summary
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
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Klesov, Oleg
Dewey number
519.2
Illustrations
illustrations
Index
index present
LC call number
QA273.67
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Probability Theory and Stochastic Modelling,
Series volume
volume 71
http://library.link/vocab/subjectName
  • Limit theorems (Probability theory)
  • Random variables
  • Mathematics
  • Probability Theory and Stochastic Processes
  • Statistical Theory and Methods
  • Mathematical Methods in Physics
  • MATHEMATICS
  • MATHEMATICS
  • Limit theorems (Probability theory)
  • Random variables
Label
Limit theorems for multi-indexed sums of random variables, Oleg Klesov
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
894498669
Dimensions
unknown
Extent
1 online resource (xviii, 483 pages)
File format
unknown
Form of item
online
Isbn
9783662443897
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-662-44388-0
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)894498669
Label
Limit theorems for multi-indexed sums of random variables, Oleg Klesov
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
894498669
Dimensions
unknown
Extent
1 online resource (xviii, 483 pages)
File format
unknown
Form of item
online
Isbn
9783662443897
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-662-44388-0
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)894498669

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