Generalized two-parameter Lebesgue-Stieltjes integrals and their applications to fractional Brownian fields

  • S. A. Il'chenko
  • Yu. S. Mishura Київ. нац. ун-т iм. Т. Шевченка

Abstract

We consider two-parameter fractional integrals and Weyl, Liouville, and Marchaut derivatives and substantiate some of their properties. We introduce the notion of generalized two-parameter Lebesgue-Stieltjes integral and present its properties and computational formulas for the case of differentiable functions. The main properties of two-parameter fractional integrals and derivatives of Hölder functions are considered. As a separate case, we study generalized two-parameter Lebesgue-Stieltjes integrals for an integrator of bounded variation. We prove that, for Hölder functions, the integrals indicated can be calculated as the limits of integral sums. As an example, generalized two-parameter integrals of fractional Brownian fields are considered.
Published
25.04.2004
How to Cite
Il’chenkoS. A., and MishuraY. S. “Generalized Two-Parameter Lebesgue-Stieltjes Integrals and Their Applications to Fractional Brownian Fields”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, no. 4, Apr. 2004, pp. 435–450, https://umj.imath.kiev.ua/index.php/umj/article/view/3766.
Section
Research articles