Pointwise dimension of archimedean copulas

Abstract

In this thesis, we introduce the pointwise dimension of a bivariate copula C at (u,v) in [0, 1]2 via its C-volume. This quantity gives a broader view of probability mass distribution than the support of a copula, the smallest closed set on which the whole mass lies. We would like to study some fundamental properties of pointwise dimension, including the equality to pointwise exponent whenever both of them exist. After that, we investigate the behavior of the pointwise dimension of copulas constructed by various methods. In the last part, we compute the pointwise dimension of Archimedean copulas, an important class of copulas used widely in many branches.