<abstract xmlns="http://www.w3.org/1999/xhtml">Motivated by the maximal average distance of uniformly distributed sequences we consider some extremal problems for functionals of type
<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_udt-2020-0013_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><msub><mrow><mi>μ</mi></mrow><mi>C</mi></msub><mo>↦</mo><mrow><msubsup><mo>∫</mo><mn>0</mn><mn>1</mn></msubsup><mrow><msub><mrow><mrow><mrow><msubsup><mo>∫</mo><mn>0</mn><mn>1</mn></msubsup><mrow><mi>F</mi><mi>d</mi></mrow></mrow></mrow></mrow><mi>μ</mi></msub><msub><mrow></mrow><mi>C</mi></msub><mo>,</mo></mrow></mrow></mrow></math><tex-math>{\mu _C} \mapsto \int_0^1 {{{\int_0^1 {Fd} }_\mu }_C,}</tex-math></alternatives></disp-formula>
where <italic>µC</italic> is a copula measure and <italic>F</italic> 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.</abstract>

Motivated by the maximal average distance of uniformly distributed sequences we consider some extremal problems for functionals of type
μC↦∫01∫01FdμC,{\mu _C} \mapsto \int_0^1 {{{\int_0^1 {Fd} }_\mu }_C,}
where µC 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.

On Extremal Problems for Pairs of Uniformly Distributed Sequences and Integrals with Respect to Copula Measures

Dipartimento di Matematica e Fisica “Ennio De Giorgi”

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Motivated by the maximal average distance of uniformly distributed sequences we consider some extremal problems for functionals of type
μC↦∫01∫01FdμC,{\mu _C}...

On Extremal Problems for Pairs of Uniformly Distributed Sequences and Integrals with Respect to Copula Measures

Online veröffentlicht: 25. Dez. 2020

Seitenbereich: 99 - 112

Eingereicht: 12. Juni 2020

Akzeptiert: 15. Nov. 2020

DOI: https://doi.org/10.2478/udt-2020-0013

Schlüsselwörter
Uniform distribution, Copulas, Extremal problems

© 2020 Fabrizio Durante et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On Extremal Problems for Pairs of Uniformly Distributed Sequences and Integrals with Respect to Copula Measures

Online veröffentlicht: 25. Dez. 2020

Seitenbereich: 99 - 112

Eingereicht: 12. Juni 2020

Akzeptiert: 15. Nov. 2020

DOI: https://doi.org/10.2478/udt-2020-0013

SchlüsselwörterUniform distribution, Copulas, Extremal problems

© 2020 Fabrizio Durante et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Schlüsselwörter
Uniform distribution, Copulas, Extremal problems