Factorizable non-atomic copulas

Tanes Printechapat and Songkiat Sumetkijakan

Statistics & Probability Letters, 2018, vol. 143, issue C, 86-94

Abstract: Generalizing the notion of invariant sets by Darsow and Olsen, Sumetkijakan studied a subclass of singular copulas, the so-called non-atomic copulas, defined via its associated σ-algebras. It was shown that the Markov operator of every non-atomic copula is partially factorizable, i.e. it is the composition of left and right invertible Markov operators on a subspace of L1([0,1]) depending on the copula. Here, we further investigate the associated σ-algebras of the product of certain copulas and obtain (1) a sharper result on the partial factorizability of non-atomic copulas and (2) the existence and uniqueness of a completely factorizable copula that shares the same set of associated σ-algebras as that of a given non-atomic copula.

Keywords: Copula; Non-atomic; Associated sigma-algebra; Factorizability; Markov operator (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2018.08.005

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