- Leadbetter, M. Ross, et al.
Conditions for the convergence in distribution of stationary normal processes
Ingår i: Stochastic Processes and their Applications. - Elsevier. - 1879-209X. ; 8:2, s. 131-139
- The asymptotic distribution of the maximum Mn=max1=<t=<nξt in a stationary normal sequence ξ1,ξ,... depends on the correlation rt between ξ0 and ξt. It is well known that if rt log t -> 0 as t -> ~ or if Σr2t<~, then the limiting distribution is the same as for a sequence of independent normal variables. Here it is shown that this also follows from a weaker condition, which only puts a restriction on the number of t-values for which rt log t islarge. The condition gives some insight into what is essential for this asymptotic behaviour of maxima. Similar results are obtained for a stationary normal process in continuous time.