Ukrainian Mathematical Journal

, Volume 50, Issue 10, pp 1551–1558 | Cite as

Asymptotic properties of the norm of the extremum of a sequence of normal random functions

  • I. K. Matsak


Under additional conditions on a bounded normally distributed random function X = X( t), t ∈ T, we establish a relation of the form
$$\mathop {\lim }\limits_{n \to \infty } P(b_n (||Z_n || - a_n ) \leqslant x) = \exp ( - e^{ - x} )\forall x \in R^1 $$
where \(Z_n = Z_n (t) = \mathop {\max }\limits_{1 \leqslant k \leqslant n} X_k (t),(X_n )\) are independent copies of \(X,||x(t)|| = \mathop {\sup }\limits_{1 \in T} |x(t)|\), and (a n) and (b n) are numerical sequences.


Weak Convergence Asymptotic Property Random Function Random Element Asymptotic Relation 
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Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • I. K. Matsak
    • 1
  1. 1.Ukrainian State Academy of Light IndustryKiev

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