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- Yi-Jun Xiao
- Monte Carlo Meth. and Appl.
- 1996

An inequality on the variation of the product of two functions of bounded variation and some applications in numerical solution of certain class of parabolic partial diierential equations by low-discrepancy sequences are given.

- Yi-Jun Xiao
- 1990

- Yi-Jun Xiao
- 2010

In this paper, we study the geometric generation of the (0; m; 2)-nets. Based on some combinatorial methods, a generation property on (0; m; 2)-nets with an applications to a Sobol' sequence and the number of the (0; m; 2)-nets in equivalent sense are given. We also present some symmetry properties of the Sobol' sequence and the Roth-Zaremba sequence.

- Yi-Jun Xiao
- 2010

In this paper, we estimate the star-diaphony and the diaphony of the Roth sequence and the Zaremba sequence using their L 2-discrepancy formula given by Halton and Zaremba (see 3]), and White (see 17]). The optimal estimates and the exact asymptotic behaviours of the star-diaphony and the diaphony of both sequences are given. Moreover, the exact asymptotic… (More)

- Yi-Jun Xiao
- 1996

In this paper, we introduce the notion of volume-discrepancy (and of isotropic volume-discrepancy) of a sequences of points and we establish some of their basic properties. This notion is illustrated by an application to a reliability problem.

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