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Introduction to Quasi-Monte Carlo Integration and Applications / by Gunther Leobacher, Friedrich Pillichshammer.
Springer Nature - Springer Mathematics and Statistics (R0) eBooks 2026 English International Available online
View online- Format:
- Book
- Author/Creator:
- Leobacher, Gunther.
- Series:
- Compact Textbooks in Mathematics, 2296-455X
- Language:
- English
- Subjects (All):
- Numerical analysis.
- Probabilities.
- Social sciences--Mathematics.
- Social sciences.
- Numerical Analysis.
- Probability Theory.
- Mathematics in Business, Economics and Finance.
- Local Subjects:
- Numerical Analysis.
- Probability Theory.
- Mathematics in Business, Economics and Finance.
- Physical Description:
- 1 online resource (410 pages)
- Edition:
- 2nd ed. 2026.
- Place of Publication:
- Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2026.
- Summary:
- 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.
- Contents:
- 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.
- ISBN:
- 3-032-05446-X
- 9783032054463
- OCLC:
- 1574120662
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