Distribution of extreme values for Gaussian sequences with a trend (Q920473)

Let \(\{X_ k+m^ n_ k\), \(1\leq k\leq n\), \(n\geq 1\}\) be a triangular array of independent standard Gaussian random variables with trend. The author gives conditions under which, for suitable normalizing constants \(\{c_ n\), \(n\geq 1\}\), \[ P\{c_ n(\max_{1\leq k\leq n}(X_ k+m^ n_ k)-c_ n)\leq x\} \] converges weakly to the double exponential distribution \(\Lambda (x)=\exp \{-e^{-x}\}\).