Introduction to Quasi-Monte Carlo Integration and Applications
Description
This textbook offers a comprehensive introduction to quasi-Monte Carlo methods and several of their applications. Throughout, the authors use modern concepts and notations to provide an overview of how the theory behind quasi-Monte Carlo methods developed. While the main focus of this text is on the theory, it also explores several applications with a particular emphasis on financial problems.
This second edition contains substantial revisions and additions, including several new sections that more thoroughly cover weighted problems. New sections include coverage of the weighted Koksma-Hlawka inequality, weighted discrepancy of lattice point sets and tractability properties, polynomial lattice point sets, and more. In addition, the authors have corrected minor errors from the first edition and updated the bibliography and "Further reading" sections.
Introduction to Quasi-Monte Carlo Integration and Applications is suitable for advanced undergraduate students in mathematics and computer science. Readers should possess a basic knowledge of algebra, calculus, linear algebra, and probability theory. It may also be used for self-study or as a reference for researchers interested in the area.
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Friedrich Pillichshammer is Associate Professor at the Institute of Financial Mathematics at the Johannes Kepler University Linz.
Gunther Leobacher is Professor of Stochastics at the Department of Mathematics and Scientific Computing at the University of Graz.
Content
Preface.- Notation.- I Introduction.- II Uniform distribution modulo one.- III QMC integration in reproducing kernel Hilbert spaces.- IV Lattice point sets.- V (t, m, s)-nets and (t, s)-sequences.- VI A short discussion of the discrepancy bounds.- VII Foundations of financial mathematics.- VIII MC and QMC simulation.