Supports of quasi-copulas

TL;DR

This paper extends the understanding of supports of copulas to quasi-copulas, demonstrating the existence of supports with specific fractal dimensions in both bivariate and multivariate cases.

Contribution

It introduces new results on the supports of quasi-copulas, generalizing previous findings from copulas to a broader class of functions.

Findings

Supports of quasi-copulas can have prescribed fractal dimensions.

Existence of quasi-copulas supported on self-similar fractal sets.

Results apply to both bivariate and multivariate quasi-copulas.

Abstract

It is known that for every $s\in]1,2[$ there is a copula whose support is a self-similar fractal set with Hausdorff -- and box-counting -- dimension $s$. In this paper we provide similar results for (proper) quasi-copulas, in both the bivariate and multivariate cases.