Maxima and minima of stationary random sequences under a local dependence restriction.
Maxima of the cells of an equiprobable multinomial.
Maximum process problems in optimal control theory.
Moments of gamma type and the Brownian supremum process area.
Multidimensional limit theorems for smoothed extreme value estimates of point processes boundaries
In this paper, we give sufficient conditions to establish central limit theorems and moderate deviation principle for a class of support estimates of empirical and Poisson point processes. The considered estimates are obtained by smoothing some bias corrected extreme values of the point process. We show how the smoothing permits to obtain Gaussian asymptotic limits and therefore pointwise confidence intervals. Some unidimensional and multidimensional examples are provided.
Multivariate tail equivalence of distributions in extreme value theory