| Title | Conditions for the convergence in distribution of stationary normal processes |
| Authors | M. Ross Leadbetter, Georg Lindgren, Holger Rootzén |
| Alternative Location | http://ida.lub.lu.se/cgi-bi..., Restricted Access |
| Publication | Stochastic Processes and their Applications |
| Year | 1978 |
| Volume | 8 |
| Issue | 2 |
| Pages | 131 - 139 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | North-Holland |
| Abstract English | 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. |
| Keywords | Mathematical Subject Codes Primary 60G15, Mathematical Subject Codes 60G10, Mathematical Subject Codes Stationary normal sequences, Mathematical Subject Codes Stationary normal processes, Mathematical Subject Codes Limit distribution for maxima, |
| ISBN/ISSN/Other | ISSN: 03044149 |
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