Asymptotic behavior of the norm of the maximum of a sequence of Gaussian random variables. (English. Ukrainian original) Zbl 0923.60007

Matsak, I. K.

Theory Probab. Math. Stat. 56, 129-136 (1998); translation from Teor. Jmovirn. Mat. Stat. 56, 126-132 (1997).

The author considers a random function \(\{ X=X(t)\), \(t\in T\}\) with Gaussian distribution. Given sequences of independent copies \(X_n, n\geq 1\), of \(X\), the author investigates \(Z_n(t)=\max_{1\leq k\leq n}X_k(t)\). The asymptotic behaviour of \(| | Z_n(t)| | =\sup_{t\in T}| Z_n(t)| \) is studied. Two examples are given.

Reviewer: A.Ya.Olenko (Kyïv)

MSC:

60B12	Limit theorems for vector-valued random variables (infinite-dimensional case)
60G15	Gaussian processes

Keywords:

random function; asymptotic behaviour; uniform norm; asymptotic normality