Multivariate extreme values in T-periodic random sequences under mild oscillation restrictions

Stochastic Processes and their Applications, 49(1) (1994), 111–125
http://dx.doi.org/10.1016/0304-4149(94)90115-5

If the sequence of partial maxima, generated by a multivariate T-periodic sequence {Xn = (Xn1, …, Xnd)}n ? 1, under an appropriate mixing condition, converges in distribution, under linear normalization, then the limit is a multivariate extreme value distribution. Sufficient conditions for the limiting independence of the components and existence of the multivariate extremal index are given. Limiting results for exceedance counts can be easily obtained from exceedance runs of {Xnj}n ? 1, j = 1, …, d.