Random and Quasi-Random Point Sets

Häftad, Engelska, 1998

Del 138 i serien Lecture Notes in Statistics

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Beskrivning

This book sumarizes recent theoretical and practical developments. The generation and the assessment of pseudo- and quasi-random point sets is one of the basic tasks of applied mathematics and statistics, with implications for Monte Carlo methods, stochastic simulation, and applied statistics. They are also of strong theoretical interest, with applications to algebraic geometry, metric number theory, probability theory, and cryptology.

Produktinformation

Utgivningsdatum:1998-10-09
Mått:155 x 235 x 19 mm
Vikt:528 g
Format:Häftad
Språk:Engelska
Serie:Lecture Notes in Statistics
Antal sidor:334
Förlag:Springer-Verlag New York Inc.
ISBN:9780387985541

Utforska kategorier

Matematisk statistik inom Naturvetenskap och teknik

Innehållsförteckning

From Probabilistic Diophantine Approximation to Quadratic Fields.- 1 Part I: Super Irregularity.- 2 Part II: Probabilistic Diophantine Approximation.- 3 Part III: Quadratic Fields and Continued Fractions.- 4 Part IV: Class Number One Problems.- 5 Part V: Cesaro Mean of % MathType!MTEF!2!1!+-% feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcqaaaaaaaaaWdbe% aadaaeqaWdaeaapeWaaeWaa8aabaWdbmaacmaapaqaa8qacaWGUbGa% eqySdegacaGL7bGaayzFaaGaeyOeI0IaaGymaiaac+cacaaIYaaaca% GLOaGaayzkaaaal8aabaWdbiaad6gaaeqaniabggHiLdaaaa!42C9!$$ \sum\nolimits_n {\left( {\left\{ {n\alpha } \right\} - 1/2} \right)} $$.- 6 References.- On the Assessment of Random and Quasi-Random Point Sets.- 1 Introduction.- 2 Chapter for the Practitioner.- 3 Mathematical Preliminaries.- 4 Uniform Distribution Modulo One.- 5 The Spectral Test.- 6 The Weighted Spectral Test.- 7 Discrepancy.- 8 Summary.- 9 Acknowledgements.- 10 References.- Lattice Rules: How Well Do They Measure Up?.- 1 Introduction.- 2 Some Basic Properties of Lattice Rules.- 3 A General Approach to Worst-Case and Average-Case Error Analysis.- 4 Examples of Other Discrepancies.- 5 Shift-Invariant Kernels and Discrepancies.- 6 Discrepancy Bounds.- 7 Discrepancies of Integration Lattices and Nets.- 8 Tractability of High Dimensional Quadrature.- 9 Discussion and Conclusion.- 10 References.- Digital Point Sets: Analysis and Application.- 1 Introduction.- 2 The Concept and Basic Properties of Digital Point Sets.- 3 Discrepancy Bounds for Digital Point Sets.- 4 Special Classes of Digital Point Sets and Quality Bounds.- 5 Digital Sequences Based on Formal Laurent Series and Non-Archimedean Diophantine Approximation.- 6 Analysis of Pseudo-Random-Number Generators by Digital Nets.- 7 The Digital Lattice Rule.- 8 Outlook and Open Research Topics.- 9 References.- Random Number Generators: Selection Criteria and Testing.- 1 Introduction.- 2 Design Principles and Figures of Merit.- 3 Empirical Statistical Tests.- 4 Examples of Empirical Tests.- 5 Collections of Small RNGs.- 6 Systematic Testing for Small RNGs.- 7 How Do Real-Life Generators Fare in These Tests?.- 8 Acknowledgements.- 9 References.- Nets, (ts)-Sequences, and Algebraic Geometry.- 1 Introduction.- 2 Basic Concepts.- 3 The Digital Method.- 4 Background on Algebraic Curves over Finite Fields.- 5 Construction of (ts)-Sequences.- 6 New Constructions of (tms)-Nets.- 7 New Algebraic Curves with Many Rational Points.- 8 References.- Financial Applications of Monte Carlo and Quasi-Monte Carlo Methods.- 1 Introduction.- 2 Monte Carlo Methods for Finance Applications.- 3 Speeding Up by Quasi-Monte Carlo Methods.- 4 Future Topics.- 5 References.