We consider the random field Mt=supn≥1−logAn+Xnt, t ∈ T, for a set T ⊂ ℝm, where (Xn) is an i.i.d. sequence of centered Gaussian random fields on T and 0 < A₁ < A₂ < · · · are the arrivals of a ...

An N-parameter Brownian sheet in ${\bf R}^{d}$ maps a non-random compact set F in ${\bf R}_{+}^{N}$ to the random compact set B(F) in ${\bf R}^{d}$ . We prove two results on the image-set B(F): (1) It ...