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Factorizable non-atomic copulas

Author

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  • Printechapat, Tanes
  • Sumetkijakan, Songkiat

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.

Suggested Citation

  • Printechapat, Tanes & Sumetkijakan, Songkiat, 2018. "Factorizable non-atomic copulas," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 86-94.
    • Handle: RePEc:eee:stapro:v:143:y:2018:i:c:p:86-94
    DOI: 10.1016/j.spl.2018.08.005
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    References listed on IDEAS

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    1. Zheng, Yanting & Yang, Jingping & Huang, Jianhua Z., 2011. "Approximation of bivariate copulas by patched bivariate Fréchet copulas," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 246-256, March.
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    Cited by:

    1. Chamnan Wongtawan & Sumetkijakan Songkiat, 2023. "Characterization of pre-idempotent Copulas," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-12, January.

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