Motivated by applications in queueing fluid models and ruin theory, we analyze the asymptotics of $\mathbb{P}(su{p}_{t\in [0,T]}({\sum }_{i=1}^n{\lambda }_i{B}_{H_i}\left(t\right)-ct)>u)$, where $B_{H_i}\left(t\right):t\ge 0$, i = 1,...,n, are independent fractional Brownian motions with Hurst parameters $H_i\in (0,1]$ and λ₁,...,λₙ > 0. The asymptotics takes one of three different qualitative forms, depending on the value of $mi{n}_{i=1,...,n}{H}_i$.

Fine regularity of stochastic processes is usually measured in a local way by local Hölder exponents and in a global way by fractal dimensions. In the case of multiparameter Gaussian random fields, Adler proved that these two concepts are connected under the assumption of increment stationarity property. The aim of this paper is to consider the case of Gaussian fields without any stationarity condition. More precisely, we prove that almost surely the Hausdorff dimensions of the range and the graph...