## Monte Carlo and Quasi-Monte Carlo Methods 1996: Proceedings of a Conference at the University of Salzburg, Austria, July 9-12, 1996Harald Niederreiter, Peter Hellekalek, Gerhard Larcher, Peter Zinterhof, Peter J. Bickel, P. Diggle, S. Fienberg, K. Krickeberg, I. Olkin Monte Carlo methods are numerical methods based on random sampling and quasi-Monte Carlo methods are their deterministic versions. This volume contains the refereed proceedings of the Second International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at the University of Salzburg (Austria) from July 9--12, 1996. The conference was a forum for recent progress in the theory and the applications of these methods. The topics covered in this volume range from theoretical issues in Monte Carlo and simulation methods, low-discrepancy point sets and sequences, lattice rules, and pseudorandom number generation to applications such as numerical integration, numerical linear algebra, integral equations, binary search, global optimization, computational physics, mathematical finance, and computer graphics. These proceedings will be of interest to graduate students and researchers in Monte Carlo and quasi-Monte Carlo methods, to numerical analysts, and to practitioners of simulation methods. |

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### Contents

A Comparison of Some Monte Carlo and Quasi Monte Carlo Techniques for Option Pricing | 1 |

a powerful tool of statistical physics | 19 |

Binary search trees based on Weyl and Lehmer sequences | 40 |

A survey of quadratic and inversive congruential pseudorandom numbers | 66 |

A Look At Multilevel Splitting | 98 |

On the Distribution of Digital Sequences | 109 |

Random Number Generators and Empirical Tests | 124 |

The AlgebraicGeometry Approach to LowDiscrepancy Sequences | 139 |

The QuasiRandom Walk | 277 |

The rate of convergence to a stable law for the random sum of iid random variables | 300 |

Some Bounds on the Figure of Merit of a Lattice Rule | 308 |

QuasiMonte Carlo integration of digitally smooth functions by digital nets | 321 |

Weak limits for the diaphony | 330 |

QuasiMonte Carlo Simulation of Random Walks in Finance | 340 |

Error Estimation for QuasiMonte Carlo Methods | 353 |

a New Class of Binary Digital t m sNets | 369 |

A Monte Carlo Estimator Based on a State Space Decomposition Methodology for Flow Network Reliability | 161 |

Monte Carlo and quasiMonte Carlo algorithms for a linear integrodifferential equation | 176 |

A Numerical Approach for Determination of Sources in Reactive Transport Equations | 189 |

Monte Carlo Algorithms for Calculating Eigenvalues | 205 |

Construction of digital nets from BCHcodes | 221 |

Computing Discrepancies Related to Spaces of Smooth Periodic Functions | 238 |

On correlation analysis of pseudorandom numbers | 251 |

Part I Matrix Problems | 382 |

QuasiMonte Carlo Methods for Integral Equations | 398 |

Quadratic Congruential Generators With Odd Composite Modulus | 415 |

A new permutation choice in Halton sequences | 427 |

Optimal UType Designs | 436 |

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### Common terms and phrases

algorithm analysis applications approach approximation assume binary bound calculated called columns Computer consider constant construction convergence corresponding defined Definition denote density depends described designs dimension discrepancy distribution elements equation error estimate example exists fact fields Figure finite function given important improved independent integration interval introduced inversive congruential iterations lattice Lemma length linear low-discrepancy Math Mathematics matrix mean measure Monte Carlo Monte Carlo methods Niederreiter Note obtained operator optimal pairs parameters path period point sets points possible presented probability problem proof properties pseudorandom numbers quadratic Quasi-Monte Carlo Methods random number random variable random walk respect rules sampling satisfies sequence shows simulation solution space standard statistical studied Table Theorem theory tree uniform University variance vector