Extreme Values and Rare Events of Non-Stationary Random Sequences
The aim of this paper is to summarize some of the recent results of extreme values in non-stationary sequences. The classical extreme value theory considers mainly the limit distributions of the maxima or minima for iid. sequences. This theory was extended consecutively by a number of papers (e.g. Watson , Loynes , Leadbetter ) to apply for a wide class of stationary sequences. The state of theory is well described in Leadbetter, Lindgren and Rootzen .
Unable to display preview. Download preview PDF.
- Hüsler, J. (1986) Extreme values of non-stationary sequences. To be published in J. Appl. Probab.Google Scholar
- Kallenberg, O. (1976) Random measures. Akademie-Verlag, Berlin, Academic Press, London-New York.Google Scholar
- Leadbetter, M.R., Lindgren, G. and Rootzen, H. (1983) Extremes and related properties of random sequences and processes. Springer, New York, Heidelberg, Berlin.Google Scholar
- Meijzler, D.G. (1956) On the problem of limit distribution for the maximal term of a variational series. L’vov Politechn. Inst. Naucn. Zp. (Fiz.-Mat.) 38, 90–109.Google Scholar
- Schüpbach, M. (1986) Limit laws for minima and maxima of nonstationary random sequences. Ph.D.thesis, University of Bern.Google Scholar
- Zähle, U. (1980) A Poisson limit theorem for rare events of a Gaussian sequence. Theory Probab. Appl. 25, 90–104.Google Scholar