Holdings: Lectures on Gaussian processes

Lectures on Gaussian processes:

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Bibliographic Details
Main Author:	Lifšic, Michail A. 1956- (Author)
Format:	Book
Language:	English
Published:	Heidelberg [u.a.] Springer 2012
Series:	Springer briefs in mathematics
Subjects:	Gauß-Prozess
Online Access:	Inhaltstext Inhaltsverzeichnis
Physical Description:	X, 121 S. 235 mm x 155 mm
ISBN:	9783642249389

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MARC


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Record in the Search Index

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adam_text	IMAGE 1 CONTENTS LECTURES ON GAUSSIAN PROCESSES 1 1 GAUSSIAN VECTORS AND DISTRIBUTIONS 1 1.1 UNI VARIATE OBJECTS 1 1.2 MULTIVARIATE OBJECTS 2 1.3 GAUSSIAN OBJECTS IN "ARBITRARY" LINEAR SPACES 5 2 EXAMPLES OF GAUSSIAN VECTORS, PROCESSES AND DISTRIBUTIONS 6 3 GAUSSIAN WHITE NOISE AND INTEGRAL REPRESENTATIONS 13 3.1 WHITE NOISE: DEFINITION AND INTEGRATION 13 3.2 INTEGRAL REPRESENTATIONS 15 4 MEASURABLE FUNCTIONALS AND THE KERNEL 22 4.1 MAIN DEFINITIONS 22 4.2 FACTORIZATION THEOREM 26 4.3 ALTERNATIVE APPROACHES TO KERNEL DEFINITION 32 5 CAMERON-MARTIN THEOREM 34 6 ISOPERIMETRIC INEQUALITY 38 6.1 EUCLIDEAN SPACE 38 6.2 EUCLIDEAN SPHERE 39 6.3 POINCARE CONSTRUCTION 40 6.4 EUCLIDEAN SPACE WITH GAUSSIAN MEASURE 41 6.5 GENERAL LINEAR SPACE WITH GAUSSIAN MEASURE 43 6.6 CONCENTRATION PRINCIPLE 43 7 MEASURE CONCAVITY AND OTHER INEQUALITIES 46 7.1 MEASURE CONCAVITY 46 7.2 DILATIONS 49 7.3 CORRELATION CONJECTURE 50 7.4 BOUNDS FOR SHIFTED MEASURES 53 8 LARGE DEVIATION PRINCIPLE 54 8.1 CRAMER-CHERNOFF THEOREM AND GENERAL LARGE DEVIATION PRINCIPLE 54 BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1016103646 DIGITALISIERT DURCH IMAGE 2 X CONTENTS 8.2 LARGE DEVIATION PRINCIPLE FOR GAUSSIAN VECTOR 56 8.3 APPLICATIONS OF LARGE DEVIATION PRINCIPLE 58 9 FUNCTIONAL LAW OF THE ITERATED LOGARITHM 61 9.1 CLASSICAL LAW OF THE ITERATED LOGARITHM 61 9.2 FUNCTIONAL LAW OF THE ITERATED LOGARITHM 62 9.3 SOME EXTENSIONS 68 9.4 STRONG INVARIANCE PRINCIPLE 70 9.5 FLIL FOR RANDOM WALK 71 10 METRIC ENTROPY AND SAMPLE PATH PROPERTIES 72 10.1 BASIC DEFINITIONS 72 10.2 UPPER BOUNDS 73 10.3 LOWER BOUNDS 77 10.4 G5-SETS AND CC-SETS 80 11 SMALL DEVIATIONS 80 11.1 DEFINITIONS AND FIRST EXAMPLES 80 11.2 MARKOV CASE 81 11.3 DIRECT ENTROPY METHOD 83 11.4 DUAL ENTROPY METHOD 88 11.5 DUALITY OF METRIC ENTROPY 92 11.6 HUBERT SPACE 93 11.7 OTHER RESULTS 95 12 EXPANSIONS OF GAUSSIAN VECTORS 96 12.1 PROBLEM SETTING 96 12.2 SERIES OF INDEPENDENT RANDOM VECTORS 96 12.3 CONSTRUCTION OF A VECTOR WITH GIVEN DISTRIBUTION 99 12.4 EXPANSION OF A GIVEN VECTOR 100 12.5 EXAMPLES: EXPANSIONS OF WIENER PROCESS 101 12.6 LINEAR OPERATORS, ASSOCIATED GAUSSIAN VECTORS, AND THEIR EXPANSIONS 105 13 QUANTIZATION OF GAUSSIAN VECTORS 106 13.1 PROBLEM SETTING 106 13.2 QUANTIZATION AND SMALL DEVIATIONS 107 14 INVITATION TO FURTHER READING 110 REFERENCES 110 INDEX 119
any_adam_object	1
author	Lifšic, Michail A. 1956-
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illustrated	Not Illustrated
indexdate	2024-07-21T00:24:03Z
institution	BVB
isbn	9783642249389
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-024737213
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physical	X, 121 S. 235 mm x 155 mm
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publisher	Springer
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series2	Springer briefs in mathematics
spelling	Lifšic, Michail A. 1956- Verfasser (DE-588)12396718X aut Lectures on Gaussian processes Mikhail Lifshits Heidelberg [u.a.] Springer 2012 X, 121 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Springer briefs in mathematics Gauß-Prozess (DE-588)4156111-9 gnd rswk-swf Gauß-Prozess (DE-588)4156111-9 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-24939-6 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3896738&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024737213&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Lifšic, Michail A. 1956- Lectures on Gaussian processes Gauß-Prozess (DE-588)4156111-9 gnd
subject_GND	(DE-588)4156111-9
title	Lectures on Gaussian processes
title_auth	Lectures on Gaussian processes
title_exact_search	Lectures on Gaussian processes
title_full	Lectures on Gaussian processes Mikhail Lifshits
title_fullStr	Lectures on Gaussian processes Mikhail Lifshits
title_full_unstemmed	Lectures on Gaussian processes Mikhail Lifshits
title_short	Lectures on Gaussian processes
title_sort	lectures on gaussian processes
topic	Gauß-Prozess (DE-588)4156111-9 gnd
topic_facet	Gauß-Prozess
url	http://deposit.dnb.de/cgi-bin/dokserv?id=3896738&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024737213&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT lifsicmichaila lecturesongaussianprocesses

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