Introduction to Quasi-Monte Carlo Integration and Applications

• Main Authors: Leobacher, Gunther (Author), Pillichshammer, Friedrich (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2014.
• Series: Compact Textbooks in Mathematics,
• Subjects: Mathematics.; Economics, Mathematical.; Numerical analysis.; Number theory.; Number Theory.; Numerical Analysis.; Quantitative Finance.

This textbook introduces readers to the basic concepts of quasi-Monte Carlo methods for numerical integration and to the theory behind them. The comprehensive treatment of the subject with detailed explanations comprises, for example, lattice rules, digital nets and sequences and discrepancy theory....

Table of Contents:

• Preface
• Notation
• 1 Introduction
• 2 Uniform Distribution Modulo One
• 3 QMC Integration in Reproducing Kernel Hilbert Spaces
• 4 Lattice Point Sets
• 5 (t, m, s)-nets and (t, s)-Sequences
• 6 A Short Discussion of the Discrepancy Bounds
• 7 Foundations of Financial Mathematics
• 8 Monte Carlo and Quasi-Monte Carlo Simulation
• Bibliography
• Index.