Holdings: Limit theorems for multi-indexed sums of random variables

Limit theorems for multi-indexed sums of random variables:

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Bibliographic Details
Main Author:	Klesov, Oleg (Author)
Format:	Electronic eBook
Language:	English
Published:	Berlin [u.a.] Springer 2014
Series:	Probability theory and stochastic modelling 71
Subjects:	Unabhängige Zufallsvariable Grenzwertsatz Electronic book text Research almost sure convergence limit theorems of probability theory multiple sums law of the iterated logarithm strong law of large numbers
Online Access:	BTU01 FRO01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract
Physical Description:	1 Online-Ressource
ISBN:	9783662443873 9783662443880
DOI:	10.1007/978-3-662-44388-0

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adam_text	LIMIT THEOREMS FOR MULTI-INDEXED SUMS OF RANDOM VARIABLES / KLESOV, OLEG : 2014 TABLE OF CONTENTS / INHALTSVERZEICHNIS 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 THESTRONG LAW OF LARGE NUMBERS 13.COMPLETE CONVERGENCE DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT. LIMIT THEOREMS FOR MULTI-INDEXED SUMS OF RANDOM VARIABLES / KLESOV, OLEG : 2014 ABSTRACT / INHALTSTEXT 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 DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
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spelling	Klesov, Oleg Verfasser (DE-588)1078697795 aut Limit theorems for multi-indexed sums of random variables Oleg Klesov Berlin [u.a.] Springer 2014 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Probability theory and stochastic modelling 71 Unabhängige Zufallsvariable (DE-588)4205983-5 gnd rswk-swf Grenzwertsatz (DE-588)4158163-5 gnd rswk-swf Electronic book text Research almost sure convergence limit theorems of probability theory multiple sums law of the iterated logarithm strong law of large numbers Grenzwertsatz (DE-588)4158163-5 s Unabhängige Zufallsvariable (DE-588)4205983-5 s DE-604 Probability theory and stochastic modelling 71 (DE-604)BV041997534 71 https://doi.org/10.1007/978-3-662-44388-0 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027646787&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027646787&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract
spellingShingle	Klesov, Oleg Limit theorems for multi-indexed sums of random variables Probability theory and stochastic modelling Unabhängige Zufallsvariable (DE-588)4205983-5 gnd Grenzwertsatz (DE-588)4158163-5 gnd
subject_GND	(DE-588)4205983-5 (DE-588)4158163-5
title	Limit theorems for multi-indexed sums of random variables
title_auth	Limit theorems for multi-indexed sums of random variables
title_exact_search	Limit theorems for multi-indexed sums of random variables
title_full	Limit theorems for multi-indexed sums of random variables Oleg Klesov
title_fullStr	Limit theorems for multi-indexed sums of random variables Oleg Klesov
title_full_unstemmed	Limit theorems for multi-indexed sums of random variables Oleg Klesov
title_short	Limit theorems for multi-indexed sums of random variables
title_sort	limit theorems for multi indexed sums of random variables
topic	Unabhängige Zufallsvariable (DE-588)4205983-5 gnd Grenzwertsatz (DE-588)4158163-5 gnd
topic_facet	Unabhängige Zufallsvariable Grenzwertsatz
url	https://doi.org/10.1007/978-3-662-44388-0 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027646787&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027646787&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV041997534
work_keys_str_mv	AT klesovoleg limittheoremsformultiindexedsumsofrandomvariables

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