57 research outputs found
ON THE LATTICE STRUCTURE OF THE ADD-WITH-CARRY AND SUBTRACT-WITH-BORROW RANDOM NUMBER GENERATORS(Workshop on Stochastic Numerics)
On High-Discrepancy Sequences
Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality九州大学21世紀COEプログラム「機能数理学の構築と展開」First, it is pointed out that the uniform distribution of points in is not always a necessary condition for every function in a proper subset of the class of all Riemann integrable functions to have the arithmetic mean of function values at the points converging to its integral over as the number of points goes to infinity. We introduce a formal definition of the -dimensional high-discrepancy sequences, which are not uniformly distributed in , and present motivation for the application of these sequences to high-dimensional numerical integration. Then, we prove that there exist non-uniform -sequences which provide the convergence rate for the integration of a certain class of -dimensional Walsh function series, where is the number of points
ANALYSIS OF THE ANOMALY OF ran10 GENERATOR IN MONTE CARLO PRICING OF FINANCIAL DERIVATIVES
Abstract Recently, Paskov reported that the use of a certain pseudo-random number generator, rani(), given in Numerical Recipes in C, First Edition makes Monte Carlo simulations for pricing financial derivatives converge to wrong values. In this paper, we trace Paskov's experiment, investigate the characteristics and the generation algorithm of the pseudo-random number generator in question, and explain why the wrong convergences occur. We then present a method for avoiding such wrong convergences. A variance reduction procedure is applied, together with a method for obtaining more precise values, and its correctness is examined. We also investigate whether statistical tests for pseudo-random numbers can detect the cause of wrong convergences. 1
Exact Cubature for a Class of Functions of Maximum Effective Dimension
We consider high dimensional integration in a broad class of functions where all elements have maximum effective dimension. We show that there exists an exact cubature with only two points. Therefore, not only the convergence but also the worst case error of quasi-Monte Carlo need not depend on the effective dimension at all
A survey of high-discrepancy sequences
This article surveys recent results and open questions on high-discrepancy sequences.MI: Global COE Program Education-and-Research Hub for Mathematics-for-IndustryグローバルCOEプログラム「マス・フォア・インダストリ教育研究拠点
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