Comparing the distribution of various suprema on two-parameter Wiener space

Abstract:

Let $Q=[0,S]\times [0,T]$ and let $C_2(Q)$ be two-parameter Wiener space. In this note we consider the ratios of the probabilities $\mathbb {P}[x(S,T)\geq c]$, $\mathbb {P}[\sup _{Q} x(s,t)\geq c]$ and $\mathbb {P}[\sup _{\partial Q} x(s,t)\geq c]$.