Uniform distribution and Quasi-Monte Carlo methods: discrepancy, integration and applications
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| Other Authors: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston, Mass.
<<De>> Gruyter
2014
|
| Series: | Radon series on computational and applied mathematics
15 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | X, 258 S. Ill. 24 cm |
| ISBN: | 9783110317893 3110317893 |
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| 245 | 1 | 0 | |a Uniform distribution and Quasi-Monte Carlo methods |b discrepancy, integration and applications |c ed. by Peter Kritzer ... |
| 264 | 1 | |a Berlin ; Boston, Mass. |b <<De>> Gruyter |c 2014 | |
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Record in the Search Index
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CONTENTS
PREFACE V
CHRISTOPH AISTLEITNER
METRIC NUMBER THEORY, LACUNARY SERIES AND SYSTEMS OF DILATED FUNCTIONS 1
1 UNIFORM DISTRIBUTION MODULO 1 2
2 METRIC NUMBER THEORY 4
3 DISCREPANCY 6
4 LACUNARY SERIES 7
5 ALMOST EVERYWHERE CONVERGENCE 10
6 SUMS INVOLVING GREATEST COMMON DIVISORS 12
JOZSEF BECK
STRONG UNIFORMITY 17
1 INTRODUCTION 17
2
SUPERUNIFORMITY AND SUPER-DUPER UNIFORMITY 26
2.1
SUPERUNIFORMITY OF THE TYPICAL BILLIARD PATHS 26
2.2
SUPER-DUPER UNIFORMITY OF THE 2-DIMENSIONAT RAY 37
3 SUPERUNIFORM MOTIONS 41
3.1
BILLIARDS IN OTHER SHAPES 41
3.2
SUPERUNIFORMITY OF THE GEODESIES ON AN EQUIFACIAL TETRAHEDRON
SURFACE 42
DMITRIY BILYK
DISCREPANCY THEORY AND HARMONIC ANALYSIS 45
1 INTRODUCTION 45
2 EXPONENTIAL SUMS 46
3 FOURIER ANALYSIS METHODS 49
3.1 ROTATED RECTANGLES 49
3.2 THE LOWER BOUND FOR CIRCLES 51
3.3 FURTHER REMARKS 53
4 DYADIC HARMONIC ANALYSIS: DISCREPANCY FUNCTION ESTIMATES 54
4.1 LADISCREPANCY, 1
P
OO 55
4.2 THE L DISCREPANCY ESTIMATES 56
4.3 THE OTHER ENDPOINT, L
1
58
HTTP://D-NB.INFO/1048115453
VIII
CONTENTS
JOSEF DICK AND FRIEDRICH PILLICHSHAMMER
EXPLICIT CONSTRUCTIONS OF POINT SETS AND SEQUENCES WITH LOW DISCREPANCY
63
1 INTRODUCTION 63
2 LOWER BOUNDS 65
3 UPPER BOUNDS 67
4 DIGITAL NETS AND SEQUENCES 69
5 WALSH SERIES EXPANSION OF THE DISCREPANCY FUNCTION 71
6 THE CONSTRUCTION OF FINITE POINT SETS ACCORDING TO CHEN AND
SKRIGANOV^*77
7 THE CONSTRUCTION OF INFINITE SEQUENCES ACCORDING TO DICK AND
PILLICHSHAMMER 79
8 EXTENSIONS TO THE L
Q
DISCREPANCY 82
9 EXTENSIONS TO ORLICZ NORMS OF THE DISCREPANCY FUNCTION 83
MICHAEL DRMOTA
SUBSEQUENCES OF AUTOMATIC SEQUENCES AND UNIFORM DISTRIBUTION 87
1 INTRODUCTION 87
2 AUTOMATIC SEQUENCES 90
3 SUBSEQUENCES ALONG THE SEQUENCE
[N
C
\
93
4 POLYNOMIAL SUBSEQUENCES 95
5 SUBSEQUENCES ALONG THE PRIMES 98
HENRI FAURE
ON ATANASSOV'S METHODS FOR DISCREPANCY BOUNDS OF LOW-DISCREPANCY
SEQUENCES 105
1 INTRODUCTION 105
2 ATANASSOV'S METHODS FOR HALTON SEQUENCES 107
2.1 REVIEW OF HALTON SEQUENCES 107
2.2 REVIEW OF PREVIOUS BOUNDS FOR THE DISCREPANCY OF HALTON
SEQUENCES 108
2.3 ATANASSOV'S METHODS APPLIED TO HALTON SEQUENCES 108
2.4 SCRAMBLING HALTON SEQUENCES WITH MATRICES 113
3 ATANASSOV'S METHOD FOR (T, S)-SEQUENCES 118
3.1 REVIEW OF
(T,
S)-SEQUENCES 118
3.2 REVIEW OF BOUNDS FOR THE DISCREPANCY OF (T, S)-SEQUENCES 119
3.3 ATANASSOV'S METHOD APPLIED TO (T, S)-SEQUENCES 119
3.4 THE SPECIAL CASE OF EVEN BASES FOR (T, S)-SEQUENCES 121
4 ATANASSOV'S METHODS FOR GENERALIZED NIEDERREITER SEQUENCES AND
(;T, E, S)- SEQUENCES 124
CONTENTS
* IX
PETER HELLEKALEK
THE HYBRID SPECTRAL TEST:
A UNIFYING CONCEPT 127
1
INTRODUCTION 127
2
ADDING DIGIT VECTORS 129
3 NOTATION 132
4
THE HYBRID SPECTRAL TEST 134
5 EXAMPLES 137
5.1 EXAMPLE 1: INTEGRATION LATTICES 137
5.2
EXAMPLE II: EXTREME AND STAR DISCREPANCY 140
PETER KRITZER, FRIEDRICH PILLICHSHAMMER, AND HENRYK WOZNIAKOWSKI
TRACTABILITY OF MULTIVARIATE ANALYTIC PROBLEMS 147
1 INTRODUCTION 147
2 TRACTABILITY 149
3 A WEIGHTED KOROBOV SPACE OF ANALYTIC FUNCTIONS 154
4 INTEGRATION IN
H(K
SA B
)
156
5 ^-APPROXIMATION IN
H(K
S A B
)
162
6 CONCLUSION AND OUTLOOK 169
GERHARD LARCHER
DISCREPANCY ESTIMATES FOR SEQUENCES:
NEW RESULTS AND OPEN PROBLEMS 171
1 INTRODUCTION 171
2 METRICAL AND AVERAGE TYPE DISCREPANCY ESTIMATES FOR DIGITAL POINT SETS
AND SEQUENCES AND FOR GOOD LATTICE POINT SETS 174
3 DISCREPANCY ESTIMATES FOR AND APPLICATIONS OF HYBRID
SEQUENCES 181
4 MISCELLANEOUS PROBLEMS 185
GUNTHER LEOBACHER
A SHORT INTRODUCTION TO QUASI-MONTE CARLO OPTION PRICING 191
1
OVERVIEW 191
2
FOUNDATIONS OF FINANCIAL MATHEMATICS *
-192
2.1
BONDS, STOCKS AND DERIVATIVES 192
2.2
ARBITRAGE AND THE NO-ARBITRAGE PRINCIPLE-
*194
2.3
THE BLACK-SCHOLES MODEL 196
2.4
SDE MODELS 197
2.5
LEVY MODELS 199
2.6
EXAMPLES 200
3
MC AND QMC SIMULATION 201
3.1
NONUNIFORM RANDOM NUMBER GENERATION -
* 201
3.2
GENERATION OF BROWNIAN PATHS 208
3.3
GENERATION OF LEVY PATHS 214
X
CONTENTS
3.4 MULTILEVEL (QUASI-)MONTE CARLO 216
3.5 EXAMPLES 218
DIRK NUYENS
THE CONSTRUCTION OF GOOD LATTICE RULES AND POLYNOMIAL LATTICE RULES 223
1 LATTICE RULES AND POLYNOMIAL LATTICE RULES 223
1.1 LATTICE RULES 224
1.2 POLYNOMIAL LATTICE RULES 225
2 THE WORST-CASE ERROR 227
2.1 KOKSMA-HLAWKA ERROR BOUND 227
2.2 LATTICE RULES 229
2.3 POLYNOMIAL LATTICE RULES 232
3 WEIGHTED WORST-CASE ERRORS 236
4 SOME STANDARD SPACES 238
4.1 LATTICE RULES AND FOURIER SPACES 238
4.2 RANDOMLY-SHIFTED LATTICE RULES AND THE UNANCHORED SOBOLEV
SPACE 239
4.3 TENT-TRANSFORMED LATTICE RULES AND THE COSINE SPACE 241
4.4 POLYNOMIAL LATTICE RULES AND WALSH SPACES 243
5 COMPONENT-BY-COMPONENT CONSTRUCTIONS 245
5.1 COMPONENT-BY-COMPONENT CONSTRUCTION 245
5.2 FAST COMPONENT-BY-COMPONENT CONSTRUCTION 249
6 CONCLUSION 252
INDEX 257 |
| any_adam_object | 1 |
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| discipline | Mathematik |
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| isbn | 9783110317893 3110317893 |
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| publisher | <<De>> Gruyter |
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| series2 | Radon series on computational and applied mathematics |
| spelling | Uniform distribution and Quasi-Monte Carlo methods discrepancy, integration and applications ed. by Peter Kritzer ... Berlin ; Boston, Mass. <<De>> Gruyter 2014 X, 258 S. Ill. 24 cm txt rdacontent n rdamedia nc rdacarrier Radon series on computational and applied mathematics 15 Literaturangaben Gleichmäßige Verteilung (DE-588)4157522-2 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Gleichmäßige Verteilung (DE-588)4157522-2 s Monte-Carlo-Simulation (DE-588)4240945-7 s DE-604 Kritzer, Peter edt Radon series on computational and applied mathematics 15 (DE-604)BV023335470 15 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4607269&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=027491892&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Uniform distribution and Quasi-Monte Carlo methods discrepancy, integration and applications Radon series on computational and applied mathematics Gleichmäßige Verteilung (DE-588)4157522-2 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| subject_GND | (DE-588)4157522-2 (DE-588)4240945-7 |
| title | Uniform distribution and Quasi-Monte Carlo methods discrepancy, integration and applications |
| title_auth | Uniform distribution and Quasi-Monte Carlo methods discrepancy, integration and applications |
| title_exact_search | Uniform distribution and Quasi-Monte Carlo methods discrepancy, integration and applications |
| title_full | Uniform distribution and Quasi-Monte Carlo methods discrepancy, integration and applications ed. by Peter Kritzer ... |
| title_fullStr | Uniform distribution and Quasi-Monte Carlo methods discrepancy, integration and applications ed. by Peter Kritzer ... |
| title_full_unstemmed | Uniform distribution and Quasi-Monte Carlo methods discrepancy, integration and applications ed. by Peter Kritzer ... |
| title_short | Uniform distribution and Quasi-Monte Carlo methods |
| title_sort | uniform distribution and quasi monte carlo methods discrepancy integration and applications |
| title_sub | discrepancy, integration and applications |
| topic | Gleichmäßige Verteilung (DE-588)4157522-2 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| topic_facet | Gleichmäßige Verteilung Monte-Carlo-Simulation |
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