Dependence, examples and tools

The talk first aims at recalling some basic facts linking independence and orthogonality structures. This will mange to provide simple conditions to model stochastic dependences. Some other simple features will also suggest a definition of weak proposed in a paper of 1999 with Sana Louhichi which has some advantages with respect to the more classical strong mixing ones as Rosenblatt’s 1956 proposed. Definitely I don’t think that only such conditions have to be used, since developing some examples, many other notions of dependence should in fact be used rather than only one. The main focus is definitely the class of models of time series of interest. A kind of botanic description will make it clear that from the point of view of examples, such weak dependence conditions (also developed in a LNS volume (with other coauthors) admits some nice features as well a a reasonable limit theory. Especially the case of integer valued models of time series has some good connection to weak dependence.