Article
On Extremal Problems for Pairs of Uniformly Distributed Sequences and Integrals With Respect to Copula Measures
Authors
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Abstract
Motivated by the maximal average distance of uniformly distributed sequences we consider some extremal problems for functionals of type
\[
\mu_C \mapsto \int_0^1\!\!\int_0^1 F \, d\mu_C,
\]
where \( \mu_C \) is a copula measure and \( F \) is a Riemann integrable function on \( [0,1]^2 \) of a specific type. Such problems have been considered in [4] and are of interest in the study of limit points of two uniformly distributed sequences.
Keywords
Uniform distribution, Copulas, Extremal problems.
Citation
Durante, F., Fernández-Sánchez, J., Ignazzi, C., & Trutschnig, W. (2020). On extremal problems for pairs of uniformly distributed sequences and integrals with respect to copula measures. Uniform Distribution Theory, 15(2), 99–112. https://doi.org/10.2478/udt-2020-0013
F. Durante, J. Fernández-Sánchez, C. Ignazzi and W. Trutschnig, “On extremal problems for pairs of uniformly distributed sequences and integrals with respect to copula measures,” Uniform Distribution Theory, vol. 15, no. 2, pp. 99–112, 2020, doi: 10.2478/udt-2020-0013.
Durante F, Fernández-Sánchez J, Ignazzi C, Trutschnig W. On extremal problems for pairs of uniformly distributed sequences and integrals with respect to copula measures. Uniform Distribution Theory. 2020;15(2):99–112. doi:10.2478/udt-2020-0013.
Durante, F., Fernández-Sánchez, J., Ignazzi, C. and Trutschnig, W. (2020), ‘On extremal problems for pairs of uniformly distributed sequences and integrals with respect to copula measures’, Uniform Distribution Theory, 15(2), pp. 99–112. Available at: https://doi.org/10.2478/udt-2020-0013.
Durante, Fabrizio, et al. “On Extremal Problems for Pairs of Uniformly Distributed Sequences and Integrals with Respect to Copula Measures.” Uniform Distribution Theory, vol. 15, no. 2, 2020, pp. 99–112. https://doi.org/10.2478/udt-2020-0013.
Durante, Fabrizio, Juan Fernández-Sánchez, Claudio Ignazzi, and Wolfgang Trutschnig. “On Extremal Problems for Pairs of Uniformly Distributed Sequences and Integrals with Respect to Copula Measures.” Uniform Distribution Theory 15, no. 2 (2020): 99–112. https://doi.org/10.2478/udt-2020-0013.
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Published by: Engineering Journals
