A note on the copulas invariant with respect to (a, b)-transformation

摘要

This paper answers the problem of copulas invariant with respect to (a, b)-transformations recently proposed by Horanska and Kolesarova (2017) [8]. Using tools from ergodic theory and iterated function systems we prove that the conjecture formulated therein is not true in general and for every (a, b) is an element of]0,1[(2) we construct a one-parametric class of nontrivial copulas invariant with respect to (a, b)-transformation. (C) 2018 Elsevier B.V. All rights reserved.