Monte Carlo and  Quasi-Monte Carlo Methods 2010 [electronic resource] /
Plaskota, Leszek.editor.
Woźniakowski, Henryk.editor.
This book represents the refereed proceedings of the Ninth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Warsaw (Poland) in August 2010. These biennial conferences are major events for Monte Carlo and the premiere event for quasi-Monte Carlo research. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. The reader will be provided with information on latest developments in these very active areas. The book is an excellent reference for theoreticians and practitioners interested in solving high-dimensional computational problems arising, in particular, in finance and statistics.
Description based upon print version of record.
Monte Carlo and Quasi-Monte Carlo Methods 2010; Preface; Contents; Part I Invited Articles; Markov Bridges, Bisection and Variance Reduction; 1 Introduction; 2 Examples; 2.1 Statistical Inference in Finite State CTMC Models; 2.2 Applications in Genetics; 3 Previous Algorithms; 4 Bisection Algorithm; 4.1 The Basic Idea; 4.2 Initialization When the Endpoints Are Equal; 4.3 Initialization When the Endpoints Are Different; 4.4 Recursion and Termination; 5 Numerical Examples; 5.1 Stratification; 5.2 Importance Sampling; 5.3 Quasi Monte Carlo; 6 Conclusions and Extensions; References
Upper Bounds in Discrepancy Theory1 Introduction; 2 A Large Discrepancy Example; 3 Monte Carlo, Quasi Monte Carlo, or Not; 4 The Classical Problem; 4.1 Two Dimensions; 4.2 Higher Dimensions; 4.3 Good Distributions; 5 Fourier-Walsh Analysis; 6 Further Reading; References; Entropy, Randomization, Derandomization, and Discrepancy; 1 Introduction; 1.1 The Star Discrepancy; 1.2 Relation to Numerical Integration; 1.3 Known Bounds for the Star Discrepancy; 1.3.1 Asymptotic Bounds; 1.3.2 Pre-Asymptotic Bounds; 1.4 Construction of Small Discrepancy Samples; 1.5 Calculating the Star Discrepancy
2 Bracketing Entropy2.1 Basic Definitions; 2.2 Construction of Bracketing Covers; 2.2.1 Cells of an Equidistant Grid; 2.2.2 Cells of a Non-equidistant Grid; 2.2.3 A Layer Construction; 2.2.4 An Essentially Optimal Construction; 2.3 Bounds for the Bracketing Number; 3 Application of Bracketing to Discrepancy; 3.1 Approximation of the Star Discrepancy; 3.2 Pre-Asymptotic Bounds via Randomization; 3.2.1 Point Sets in the d-Dimensional Unit Cube; 3.2.2 Infinite Dimensional Infinite Sequences; 3.2.3 Hybrid-Monte Carlo Sequences; 3.3 Small Discrepancy Samples via Derandomization
4 ANOVA Decomposition and Projection-Dependent Weights
Includes bibliographical references and index.
This book represents the refereed proceedings of the Ninth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Warsaw (Poland) in August 2010. These biennial conferences are major events for Monte Carlo and the premiere event for quasi-Monte Carlo research. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. The reader will be provided with information on latest developments in these very active areas. The book is an excellent reference for theoreticians and practitioners interested in solving high-dimensional computational problems arising, in particular, in finance and statistics.
Computer mathematics.
Algorithms.
Economics, Mathematical .
Applied mathematics.
Engineering mathematics.
Quantum computers.
Computational Mathematics and Numerical Analysis.
Algorithm Analysis and Problem Complexity.
Quantitative Finance.
Applications of Mathematics.
Quantum Computing.