The distribution of the maximum of particular random fields (Q1083119)

The authors consider the zero mean Gaussian random field X(t,s) with correlation function \[ R(\tau,\sigma)=EX(t,s)X(t+\tau,s+\sigma)=2^{- 1}[(1-| \tau |)^++(1-| \sigma |)^+]. \] They call it Slepian sum field. The distribution of max\(\{\) X(t,s),\(0\leq s,t\leq 1\}\) is evaluated. A special example is the process \(W(t,s)=2^{-1/2}(W_ 1(t)+W_ 2(s))\) where \(W_ 1\) and \(W_ 2\) are independent Wiener processes.