Sequences, discrepancies and applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
1997
|
| Series: | Lecture notes in mathematics
1651 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 503 S. |
| ISBN: | 3540626069 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface VII
Contents XI
1 Discrepancy of Sequences 1
1.1 Basic Concepts 1
1.1.1 Basic Definitions 1
1.1.2 Discrepancies 4
1.1.3 Dispersions 11
Notes 13
1.2 Exponential Sums 14
1.2.1 Weyl s Criterion 14
1.2.2 Erdos Turan Koksma s Inequality 15
1.2.3 LeVeque s Inequality and Diaphony 23
Notes 26
1.3 Lower Bounds 29
1.3.1 Roth s Theorem 29
1.3.2 Schmidt s Bound 40
1.3.3 Beck s Theorem 44
Notes 46
1.4 Special Sequences 48
1.4.1 (na) Sequence 48
1.4.2 KRONECKER Sequence 66
1.4.3 Digital Sequences 91
1.4.4 Normal Numbers 104
1.4.5 Exponential Sequences 118
Notes 131
1.5 Distribution Functions 138
1.5.1 Basic Concepts and Maldistribution 138
1.5.2 Distribution Functions and Recurring Sequences 142
1.5.3 Subdivisions 151
Notes 153
XII
1.6 Metric Theory 154
1.6.1 Erdos Gal Koksma s Method 154
1.6.2 Lacunary Sequences 161
1.6.3 Completely Uniformly Distributed Sequences 188
1.6.4 Philipp s Theorem 197
Notes 198
2 General Concepts of Uniform Distribution 204
2.1 Geometric Concepts of Discrepancy 204
2.1.1 Discrepancy Systems 204
2.1.2 Euclidean Discrepancy Systems 212
2.1.3 Spherical Discrepancy Systems 231
2.1.4 Alexander s Method 241
Notes 248
2.2 Summation Methods 249
2.2.1 Weighted Means 249
2.2.2 Well Distribution 259
2.2.3 Abel s Summation Method 268
Notes 275
2.3 Continuous Uniform Distribution 277
2.3.1 Basic Results 277
2.3.2 Discrepancy Bounds 288
2.3.3 Metric Results 300
Notes 312
2.4 Uniform Distribution in Abstract and Discrete Spaces 313
2.4.1 Uniform Distribution in Compact and Locally Compact Spaces 313
2.4.2 Distribution Problems in Finite Sets 317
2.4.3 Combinatorial Concepts of Discrepancy 340
2.4.4 Linear Recurring Sequences 346
Notes 362
3 Applications 368
3.1 Numerical Integration, Approximation, and Mathematical Finance . . 368
3.1.1 Integration and Approximation of Continuous Functions .... 368
3.1.2 Nets and (t,s) sequences 381
3.1.3 Mathematical Finance 387
3.1.4 Average Case Analysis 390
Notes 396
3.2 Spherical Problems 399
3.2.1 Spherical Designs and Chebyshev Quadrature 399
3.2.2 Slice Dispersion and Polygonal Approximation of Curves .... 406
Notes 410
XIII
3.3 Partial Differential Equations 410
3.3.1 The Heat Equation 410
3.3.2 The Boltzmann Equation 414
3.3.3 The Fourier Approach 419
Notes 423
3.4 Random Number Generators 424
3.4.1 Basic Concepts of Randomness 424
3.4.2 Examples of Number Theoretic Generators 426
Notes 431
Bibliography 433
List of Symbols 498
Subject Index 500
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:05:46Z |
| institution | BVB |
| isbn | 3540626069 |
| language | German |
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| physical | XIII, 503 S. |
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| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Drmota, Michael 1964- Verfasser (DE-588)131835718 aut Sequences, discrepancies and applications Michael Drmota ; Robert F. Tichy Berlin [u.a.] Springer 1997 XIII, 503 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1651 Sequences (Mathematics) Uniform distribution (Probability theory) Folge Mathematik (DE-588)4017790-7 gnd rswk-swf Gleichverteilung (DE-588)4157566-0 gnd rswk-swf Verteilung modulo 1 (DE-588)4331460-0 gnd rswk-swf Folge Mathematik (DE-588)4017790-7 s Verteilung modulo 1 (DE-588)4331460-0 s DE-604 Gleichverteilung (DE-588)4157566-0 s Tichy, Robert F. 1957- Verfasser (DE-588)131835769 aut Lecture notes in mathematics 1651 (DE-604)BV000676446 1651 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007516177&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Drmota, Michael 1964- Tichy, Robert F. 1957- Sequences, discrepancies and applications Lecture notes in mathematics Sequences (Mathematics) Uniform distribution (Probability theory) Folge Mathematik (DE-588)4017790-7 gnd Gleichverteilung (DE-588)4157566-0 gnd Verteilung modulo 1 (DE-588)4331460-0 gnd |
| subject_GND | (DE-588)4017790-7 (DE-588)4157566-0 (DE-588)4331460-0 |
| title | Sequences, discrepancies and applications |
| title_auth | Sequences, discrepancies and applications |
| title_exact_search | Sequences, discrepancies and applications |
| title_full | Sequences, discrepancies and applications Michael Drmota ; Robert F. Tichy |
| title_fullStr | Sequences, discrepancies and applications Michael Drmota ; Robert F. Tichy |
| title_full_unstemmed | Sequences, discrepancies and applications Michael Drmota ; Robert F. Tichy |
| title_short | Sequences, discrepancies and applications |
| title_sort | sequences discrepancies and applications |
| topic | Sequences (Mathematics) Uniform distribution (Probability theory) Folge Mathematik (DE-588)4017790-7 gnd Gleichverteilung (DE-588)4157566-0 gnd Verteilung modulo 1 (DE-588)4331460-0 gnd |
| topic_facet | Sequences (Mathematics) Uniform distribution (Probability theory) Folge Mathematik Gleichverteilung Verteilung modulo 1 |
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