8 citations · 8 across the 3 of their papers we have counts for
6 papers
On corner avoidance of -adic Halton sequences
Markus Hofer, Volker Ziegler
We consider the corner avoiding property of -dimensional -adic Halton sequences. After extending this class of point sequences in an intuitive way, we show that t…
Optimal Bounds for Integrals with Respect to Copulas and Applications
Markus Hofer, Maria Rita Iacò
We consider the integration of two-dimensional, piecewise constant functions with respect to copulas. By drawing a connection to linear assignment problems, we can give optimal upp…
A central limit theorem for Latin hypercube sampling with dependence and application to exotic basket option pricing
Christoph Aistleitner, Markus Hofer, Robert Tichy
We consider the problem of estimating , where denotes a random vector with uniformly distributed marginals. In general, Latin…
Ergodic properties of β-adic Halton sequences
Markus Hofer, Maria Rita Iacò, Robert Tichy
We investigate a parametric extension of the classical s-dimensional Halton sequence, where the bases are special Pisot numbers. In a one- dimensional setting the properties of suc…
On the uniform distribution modulo 1 of multidimensional LS-sequences
Christoph Aistleitner, Markus Hofer, Volker Ziegler
Ingrid Carbone introduced the notion of so-called LS-sequences of points, which are obtained by a generalization of Kakutani's interval splitting procedure. Under an appropriate ch…
Probabilistic discrepancy bound for Monte Carlo point sets
Christoph Aistleitner, Markus Hofer
By a profound result of Heinrich, Novak, Wasilkowski, and Wo{ź}niakowski the inverse of the star-discrepancy $n^*(s,\ve)$ satisfies the upper bound $n^*(s,\ve) \leq c_{\mathrm{abs}…