Semicontinuous processes in multi-dimensional extreme value theory
The author provides a new framework for weak convergence of extremes for stationary random fields. He extends some well-known results in the one- dimensional theory, which can be found in the monograph by \textit{M. R. Leadbetter}, \textit{G. Lindgren} and \textit{H. Rootzén}, Extreme and related problems of random sequences and processes (1983; Zbl 0518.60021), to random fields. The emphasis is on the continuous-parameter case, although new results are obtained also for discrete parameter random fields. Concrete asymptotic results are given for the Gaussian fields. The main tools are some recent results of \textit{W. Vervaat} [cf. Random upper semicontinuous functions and extremal processes, Report MS-R8801, Centre for Mathematics and Computer Science, Amsterdam (1988)] and the author [Ann. Probab. 12, 726-732 (1984; Zbl 0545.60021) and Probab. Theory Relat. Fields 73, 281-297 (1986; Zbl 0581.60042)], concerning semicontinuous processes and random sets.
weak convergence of extremes for stationary random fields
scientific article; zbMATH DE number 4022265
scientific article