Asymptotic properties of the norm of extremum values of normal random elements in the space C[0, 1] - Matsak, I. K. (Ukrains’kyi Matematychnyi Zhurnal, 1998)
We prove that _n → ∞ ( \| Z_n \| - (2 ln (n))^1/2 \| σ \| ) = 0 a.s., where X is a normal random element in the space C [0,1], MX = 0, σ = (M¦X(t)¦2)1/2 t∈[0,1, (X n ) are independent copies of X, and \(Z_n = _l k n X_k \) . Under additional restrictions on the random element X, this equality can be strengthened.