Lectures on Gaussian processes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Heidelberg [u.a.]
Springer
2012
|
| Schriftenreihe: | Springer briefs in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | X, 121 S. 235 mm x 155 mm |
| ISBN: | 9783642249389 |
Internformat
MARC
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Datensatz im Suchindex
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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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| author_facet | Lifšic, Michail A. 1956- |
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| ctrlnum | (OCoLC)766342889 (DE-599)DNB1016103646 |
| dewey-full | 519.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.23 |
| dewey-search | 519.23 |
| dewey-sort | 3519.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV039878028 |
| 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 |
| publishDate | 2012 |
| publishDateSearch | 2012 |
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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 |
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