The Resource Limit theorems for multiindexed sums of random variables, Oleg Klesov
Limit theorems for multiindexed sums of random variables, Oleg Klesov
Resource Information
The item Limit theorems for multiindexed sums of random variables, Oleg Klesov represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Limit theorems for multiindexed sums of random variables, Oleg Klesov represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 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 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
 Language
 eng
 Extent
 1 online resource (xviii, 483 pages)
 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 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
 Isbn
 9783662443897
 Label
 Limit theorems for multiindexed sums of random variables
 Title
 Limit theorems for multiindexed sums of random variables
 Statement of responsibility
 Oleg Klesov
 Subject

 Limit theorems (Probability theory)
 MATHEMATICS  Applied
 MATHEMATICS  Probability & Statistics  General
 Mathematical Methods in Physics
 Mathematics
 Probability Theory and Stochastic Processes
 Random variables
 Random variables
 Random variables
 Statistical Theory and Methods
 Limit theorems (Probability theory)
 Limit theorems (Probability theory)
 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 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
 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 multiindexed sums of random variables, Oleg Klesov
 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 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
 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
 10.1007/9783662443880
 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 multiindexed sums of random variables, Oleg Klesov
 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 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
 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
 10.1007/9783662443880
 Other physical details
 illustrations.
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)894498669
Subject
 Limit theorems (Probability theory)
 MATHEMATICS  Applied
 MATHEMATICS  Probability & Statistics  General
 Mathematical Methods in Physics
 Mathematics
 Probability Theory and Stochastic Processes
 Random variables
 Random variables
 Random variables
 Statistical Theory and Methods
 Limit theorems (Probability theory)
 Limit theorems (Probability theory)
Member of
 Probability theory and stochastic modelling, volume 71
 Probability theory and stochastic modelling, volume 71.
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