Asymptotic properties of the norm of the extremum of a sequence of normal random functions - Matsak, I. K. (Ukrains’kyi Matematychnyi Zhurnal, 1998)
Under additional conditions on a bounded normally distributed random function X = X( t), t ∈ T, we establish a relation of the form _n → ∞ P(b_n (||Z_n || - a_n ) x) = ( - e^ - x )x R^1 where \(Z_n = Z_n (t) = _1 k n X_k (t),(X_n )\) are independent copies of \(X,||x(t)|| = _1 T |x(t)|\) , and (a n) and (b n) are numerical sequences.