PreprintCC BY 4.0arXiv
On diagonal sections of Markov products of copulas
Abstract
Given a bivariate copula C, the bivariate copula Ψ(C) is defined as the Markov product of CT and C. In this paper we consider the diagonal section of Ψ(C) under the additional assumption that its value at a single point is known. We determine the exact upper and lower bounds for the diagonal section of Ψ(C), given that Ψ(C)(a,a)=d ∈ [a2,a], where a ∈ [0,1] is a fixed point. Furthermore, we describe some additional properties of the transformation Ψ, such as its behavior under ordinal sums and the survival operation. We also study checkerboard copulas in the range of Ψ and matrices associated to them.
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BibTeX
@misc{drnovsek2026diagonal,
title = {{On diagonal sections of Markov products of copulas}},
author = {Roman Drnovšek and Damjana Kokol Bukovšek and Nik Stopar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13846},
eprint = {2610.13846},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13846},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On diagonal sections of Markov products of copulas
AU - Roman Drnovšek
AU - Damjana Kokol Bukovšek
AU - Nik Stopar
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13846
UR - https://arxiv.org/abs/2610.13846
AB - Given a bivariate copula C, the bivariate copula Ψ(C) is defined as the Markov product of C^T and C. In this paper we consider the diagonal section of Ψ(C) under the additional assumption that its value at a single point is known. We determine the exact upper and lower bounds for the diagonal section of Ψ(C), given that Ψ(C)(a,a)=d ∈ [a^2,a], where a ∈ [0,1] is a fixed point. Furthermore, we describe some additional properties of the transformation Ψ, such as its behavior under ordinal sums and the survival operation. We also study checkerboard copulas in the range of Ψ and matrices associated to them.
ER -