Probabilistic weighted star discrepancy bound based on the general equal measure partition.

In this paper, we consider the estimation of the weighted star discrepancy. A better weighted probabilistic star discrepancy bound than the use of plain Monte Carlo point sets is provided in terms of convergence order, i.e. the convergence order of the weighted probabilistic bound is improved from $ O(N^{-\frac {1}{2}}) $ O (N − 1 2 ) to $ O(N^{-\frac {1}{2}-\frac {1}{2d}}\cdot \ln ^{{1}/{2}}{N}) $ O (N − 1 2 − 1 2 d ⋅ ln 1 / 2 ⁡ N). [ABSTRACT FROM AUTHOR]