We investigate a parametric extension of the classical s-dimensional Halton sequence, where the bases are special Pisot numbers. In a onedimensional setting the properties of such sequences have already been investigated by several authors [5,8,23,28]. We use methods from ergodic theory to in order to investigate the distribution behavior of multidimensional versions of such sequences. As a consequence it is shown that the Kakutani-Fibonacci transformation is uniquely ergodic.

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 upper and lower bounds for such integrals and construct the copulas for which these bounds are attained. Furthermore, we show how our approach can be extended in order to approximate extremal values in very general situations. Finally, we apply our approximation technique to problems in financial mathematics and uniform distribution theory, such as the model-independent pricing of first-to-default swaps.

In this paper we consider the sequence of Kakutani's α-refinements corresponding to the inverse of the golden ratio (which we call the Kakutani-Fibonacci sequence of partitions) and associate to it an ergodic interval exchange (which we call the Kakutani-Fibonacci transformation) using the 'cutting-stacking' technique. We prove that the orbit of the origin under this map coincides with a low discrepancy sequence (which we call the Kakutani-Fibonacci sequence of points), which has also been considered by other authors.

Encouraged by the study of extremal limits for sums of the formwith uniformly distributed sequences {xn}, {yn} the following extremal problem is of interestfor probability measures γ on the unit square with uniform marginals, i.e., measures whose distribution function is a copula. The aim of this article is to relate this problem to combinatorial optimization and to the theory of optimal transport. Using different characterizations of maximizing γ's one can give alternative proofs of some results from the field of uniform distribution theory and beyond that treat additional questions. Finally, some applications to mathematical finance are addressed.

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ABSTRACT. The LS-sequences are a parametric family of sequences of points in the unit interval. They were introduced by Carbone [4], who also proved that under an appropriate choice of the parameters L and S, such sequences are lowdiscrepancy. The aim of the present paper is to provide explicit constants in the bounds of the discrepancy of LS-sequences. Further, we generalize the construction of Carbone [4] and construct a new class of sequences of points in the unit interval, the generalized LS-sequences.

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