  This paper deals with dependence across marginally exponentially distributed
arrival times, such as default times in financial modeling or inter-failure
times in reliability theory. We explore the relationship between dependence and
the possibility to sample final multivariate survival in a long time-interval
as a sequence of iterations of local multivariate survivals along a partition
of the total time interval. We find that this is possible under a form of
multivariate lack of memory that is linked to a property of the survival times
copula. This property defines a "self-chaining-copula", and we show that this
coincides with the extreme value copulas characterization. The self-chaining
condition is satisfied by the Gumbel-Hougaard copula, a full characterization
of self chaining copulas in the Archimedean family, and by the Marshall-Olkin
copula. The result has important practical implications for consistent
single-step and multi-step simulation of multivariate arrival times in a way
that does not destroy dependency through iterations, as happens when
inconsistently iterating a Gaussian copula.
