ON THE EVOLUTION OF COPULAS

This article reports our recent studies on the evolution of copulas. As is well known, a copula provides a flexible tool for investigating dependence relations among random variables. Except for a few cases, however, copulas are concerned mainly with the static problems, not with the time-dependent ones. On the other hand, we have introduced the concept of the evolution of copulas, which claims that a copula itself evolves according to the time variable. We review our establishments as well as drawbacks on this topic.1.Introduction 2.Evolution of Copulas 3.Evolution of copulas in discrete processes 4.Generalizations 5.DiscussionsCollaborate Research Meeting of Institute of Mathematics for Industry & MEXT collaborative workshop of mathematics and mathematical sciences with various sciences and industrial technologies 2015Multiscale Mathematics : Hierarchy of collective phenomena and interrelations between hierarchical structure

ON THE EVOLUTION OF COPULAS

1.Introduction 2.Evolution of Copulas 3.Evolution of copulas in discrete processes 4.Generalizations 5.DiscussionsCollaborate Research Meeting of Institute of Mathematics for Industry & MEXT collaborative workshop of mathematics and mathematical sciences with various sciences and industrial technologies 2015Multiscale Mathematics : Hierarchy of collective phenomena and interrelations between hierarchical structuresThis article reports our recent studies on the evolution of copulas. As is well known, a copula provides a flexible tool for investigating dependence relations among random variables. Except for a few cases, however, copulas are concerned mainly with the static problems, not with the time-dependent ones. On the other hand, we have introduced the concept of the evolution of copulas, which claims that a copula itself evolves according to the time variable. We review our establishments as well as drawbacks on this topic