Record Values in Archimedean Copula Processes

We investigate the asymptotic behavior of record values X(n) for some types of Archimedean copula processes. It is shown that the set of all limit distribution functions for X(n),normed and centered in a suitable way, under some restrictions on parameters of these processes, coincides with the corresponding set of asymptotic distributions of record values in the sequences of i.i.d. random variables.