Embedding in extremal processes and the asymptotic behavior of sums of minima
We study the asymptotic behavior of sums of minima of positive i.i.d. r.v.'s. Strong convergence, a weak invariance principle and a law of iterated logarithms are obtained. Our approach is based on the embedding of partial maxima of i.i.d. r.v.'s in a suitable extremal process, and uses a simple asymptotic relationship between record times and jump times of the extremal process.
scientific article; zbMATH DE number 4122962