Mixing sequences of random variables and probabilistic number theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
1971
|
| Series: | American Mathematical Society: Memoirs of the American Mathematical Society
114 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 102 S. |
| ISBN: | 0821818147 |
Staff View
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| 245 | 1 | 0 | |a Mixing sequences of random variables and probabilistic number theory |c by Walter Philipp |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 1971 | |
| 300 | |a 102 S. | ||
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| 650 | 4 | |a Probabilistic number theory | |
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Record in the Search Index
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| adam_text | Walter Philipp
CONTENTS
Page
Introduction X
1. Limit theorems for mixing sequences of random variables .... 3
1.1. The central problem 3
1.2. The central limit theorem with remainder and the law
of the iterated logarithm 14
1.5. An extension of the law of the iterated logarithm .... 17
1.3.1. The upper bound 18
1.3.2. The lower bound 29
2. Limit theorems for continued fractions and related algorithms . 37
3. Limit theorems in Diophantine approximation . . 42
3.1. Introduction 42
3.2. Preliminaries 45
3.3. The asymptotic behavior of N* 46
3.3.1. Preparatory remarks 46
3.3.2. The law of the iterated logarithm and the
central limit theorem for the y^ s and
the z »s ° 52
3.3.3. Proof of Theorem 3.1.2* 54
3.3.4. Proof of Theorem 3.1.1* 59
3.4. The asymptotic behavior of N 61
^. The law of the iterated logarithm for discrepancies of
sequences uniformly distributed mod 1 65
4.1. The discrepancies of almost all sequences (in the
sense of the infinite product measure). • • n 65
4.2. The discrepancies of sequences of the type T x . . . 67
5. The distribution of additive functions 73
5.1. Kubilius fundamental lemma 73
5.2. Preparatory lemmas 80
5.3. Limit theorems for additive functions of class H . . . . 86
5.4. a more direct method 95
5.5. A result on uniform distribution 95
References 99
|
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| dewey-full | 512/.7 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV005707800 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:33:26Z |
| institution | BVB |
| isbn | 0821818147 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003565621 |
| oclc_num | 197693 |
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| physical | 102 S. |
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| publishDate | 1971 |
| publishDateSearch | 1971 |
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| publisher | American Mathematical Society |
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| series | American Mathematical Society: Memoirs of the American Mathematical Society |
| series2 | American Mathematical Society: Memoirs of the American Mathematical Society |
| spelling | Philipp, Walter 1936-2006 Verfasser (DE-588)135969840 aut Mixing sequences of random variables and probabilistic number theory by Walter Philipp Providence, RI American Mathematical Society 1971 102 S. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Memoirs of the American Mathematical Society 114 Nombres, Théorie des Suites (Mathématiques) approximation diophantienne inriac probabilité inriac variable aléatoire inriac Probabilistic number theory Random variables Sequences (Mathematics) Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Zufallsvariable (DE-588)4129514-6 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 Zufallsvariable (DE-588)4129514-6 s American Mathematical Society: Memoirs of the American Mathematical Society 114 (DE-604)BV008000141 114 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003565621&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Philipp, Walter 1936-2006 Mixing sequences of random variables and probabilistic number theory American Mathematical Society: Memoirs of the American Mathematical Society Nombres, Théorie des Suites (Mathématiques) approximation diophantienne inriac probabilité inriac variable aléatoire inriac Probabilistic number theory Random variables Sequences (Mathematics) Zahlentheorie (DE-588)4067277-3 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Zufallsvariable (DE-588)4129514-6 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4064324-4 (DE-588)4129514-6 |
| title | Mixing sequences of random variables and probabilistic number theory |
| title_auth | Mixing sequences of random variables and probabilistic number theory |
| title_exact_search | Mixing sequences of random variables and probabilistic number theory |
| title_full | Mixing sequences of random variables and probabilistic number theory by Walter Philipp |
| title_fullStr | Mixing sequences of random variables and probabilistic number theory by Walter Philipp |
| title_full_unstemmed | Mixing sequences of random variables and probabilistic number theory by Walter Philipp |
| title_short | Mixing sequences of random variables and probabilistic number theory |
| title_sort | mixing sequences of random variables and probabilistic number theory |
| topic | Nombres, Théorie des Suites (Mathématiques) approximation diophantienne inriac probabilité inriac variable aléatoire inriac Probabilistic number theory Random variables Sequences (Mathematics) Zahlentheorie (DE-588)4067277-3 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Zufallsvariable (DE-588)4129514-6 gnd |
| topic_facet | Nombres, Théorie des Suites (Mathématiques) approximation diophantienne probabilité variable aléatoire Probabilistic number theory Random variables Sequences (Mathematics) Zahlentheorie Wahrscheinlichkeitsrechnung Zufallsvariable |
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