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...

Let {χk(t),t≥0} be a stationary χ-process with k degrees of freedom being independent of some non-negative random variable T. In this paper we derive the exact asymptotics of P{supt∈[0,T]χk(t)u} as u→∞ when T has a regularly varying tail with index λ∈[0,1). Three other novel...