  The convergence of properly time-scaled and normalized maxima of independent
standard Brownian motions to the Brown-Resnick process is well-known in the
literature. In this paper, we study the extremal functional behavior of
non-Gaussian processes, namely squared Bessel processes and scalar products of
Brownian motions. It is shown that maxima of independent samples of those
processes converge weakly on the space of continuous functions to the
Brown-Resnick process.
