Random Number Generationand Quasi-Monte Carlo Methods

Random Number Generation and Quasi-Monte Carlo Methods

This is an essential text on quasi-random numbers. Neiderreiter is a leading researcher in the field, and much of the work presented is his own. He covers discrepancy measures, low-discrepancy point sets, nets and (t,s)-sequences, lattices, random number generation, and random vector generation.

The material on random number and vector generation is outdated, but the rest of the book represents the foundations of today's quasi-Monte Carlo methods. This is a difficult book to read. Neiderreiter makes extensive use of finite field theory and other branches of mathematics that are not common fare, even for financial engineers. If you are going to work with quasi-random numbers, you should read this book.

Contents

1. Monte Carlo Methods and Quasi-Monte Carlo Methods

Monte Carlo methods

Quasi-Monte Carlo methods

2. Quasi-Monte Carlo Methods for Numerical Integration

Discrepancy

Error bounds

3. Low-Discrepancy Point Sets and Sequences

Classical constructions

General discrepancy bounds

4. Nets and (t,s)-Sequences

Definitions and discrepancy bounds

Combinatorial connections

General construction principles

A special construction of nets

A special construction of (t,s)-sequences

5. Lattice Rules for Numerical Integration

The method of good lattice points

Existence theorems for good lattice points

General lattice rules and their classification

Existence theorems for efficient lattice rules

6. Quasi-Monte Carlo Methods for Optimization

General theory of quasirandom search methods

Low-dispersion point sets and sequences

7. Random Numbers and Pseudorandom Numbers

Random number generation

Pseudorandom numbers

Classical generators

8. Nonlinear Congruential Pseudorandom Numbers

The general nonlinear congruential method

The inversive congruential method

9. Shift-Register Pseudorandom Numbers

The digital multistep method

The generalized feedback shift-register (GFSR) method

10. Pseudorandom Vector Generation

The matrix method

Nonlinear methods

For related books, see sections:

Math - Probability

Math - Monte Carlo Method

Financial Engineering - Numerical Methods


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