Skip to content
DraconiticResearch
Search Sources API
186,086 studies31 sourcesUpdated 58 min ago
PreprintCC BY 4.0arXiv

Couplings with prescribed maxima: A short proof of the quasi-copula characterization

  • Jonathan Ansari
Open at sourcePDFDOICite

Abstract

We provide a short probabilistic proof of the classical characterization of multivariate quasi-copulas, addressing the call for a simpler and more transparent proof expressed by Sempi (2017). Our approach is based on a coupling construction for random variables with fixed marginal distributions and a prescribed distribution of their maximum. In our main result, we show that such a coupling exists if and only if the maximum is stochastically no smaller than each component and the distribution of the maximum is dominated by the sum of the marginal measures. The construction applies to arbitrary distributions and relies only on a decomposition of the maximum law and monotone quantile couplings. A direct consequence of our main result is the existence of copulas with prescribed values along an increasing track.

Related

  1. Short-time existence and uniqueness for two-phase harmonic map heat flow with a prescribed moving interface
    Xingyu Wang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. Linear stability and divisibility gaps for Gaussian maxima
    Chahel Paatur
    arXivPreprintCC BY 4.0Full textProbabilityarXiv
  3. Maxima of the Q-index: Forbidden an odd wheel
    Hongyu Wang, Yue Ma
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  4. The β=2 partition function of Dirichlet L-functions and typical maxima
    Christopher Atherfold
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryProbabilityarXiv
  5. Local Maxima of Discrete Gaussian Processes: Exact Distributions and Infill Limits
    Dan Cheng, John Ginos
    arXivPreprintCC BY 4.0Full textProbabilityarXiv

Cite

BibTeXRIS
BibTeX
@misc{ansari2026couplings,
  title = {{Couplings with prescribed maxima: A short proof of the quasi-copula characterization}},
  author = {Jonathan Ansari},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30642},
  eprint = {2610.30642},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30642},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Couplings with prescribed maxima: A short proof of the quasi-copula characterization
AU  - Jonathan Ansari
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.30642
UR  - https://arxiv.org/abs/2610.30642
AB  - We provide a short probabilistic proof of the classical characterization of multivariate quasi-copulas, addressing the call for a simpler and more transparent proof expressed by Sempi (2017). Our approach is based on a coupling construction for random variables with fixed marginal distributions and a prescribed distribution of their maximum. In our main result, we show that such a coupling exists if and only if the maximum is stochastically no smaller than each component and the distribution of the maximum is dominated by the sum of the marginal measures. The construction applies to arbitrary distributions and relies only on a decomposition of the maximum law and monotone quantile couplings. A direct consequence of our main result is the existence of copulas with prescribed values along an increasing track.
ER  -