Friday, July 18

3:15 PM-5:15 PM
Terman Auditorium

Quasi-Monte Carlo Methods

Monte Carlo (MC) methods have long been used for high dimensional integration and simulation. One important area of current practical application is problems in finance. In order to improve the accuracy of MC methods the random samples may be replaced by more uniformly distributed sets of deterministic (quasi-random) points. This leads to quasi-Monte Carlo (qMC) methods. Current research is focused on suitable measures of uniformity, on generating better quasi-random sets (especially in high dimensions), on hybrids of MC and qMC methods, and on applications to problems in finance and physics. This mini-symposium will present some recent results in these areas and identify unsolved problems.

The purpose and intended audience of this mini-symposium are two-fold. We expect to attract practitioners, those who might use qMC methods to solve problems arising from financial or physical models. We will inform them of some of the new sets of quasi-random points, new qMC methods and practical error estimates and error bounds. The first talk will focus specifically on applications. We also expect to attract theorists who would be interested in researching some of the unsolved problems. By presenting in a nutshell some of the latest results and identifying unsolved problems they will be able to enter the field more easily.

Organizers: Fred J. Hickernell, Hong Kong Baptist University, Hong Kong; and Art B. Owen, Stanford University

3:15 Quasi-Monte Carlo Computations Using the Brownian Bridge
Russel E. Caflisch, University of California, Los Angeles
3:45 Construction and Analysis of Low Discrepancy Point Sets
Gerhard Larcher, University of Salzburg, Austria
4:15 Monte Carlo Improvement of Quasi-Monte Carlo Integration
Art B. Owen, Organizer
4:45 Quasi-Monte Carlo Error Bounds and the Efficiency of Nets
Fred J. Hickernell, Organizer

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MMD, 6/2/97