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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
Article

Abstract

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.

Keywords

Weak Convergence Asymptotic Property Random Function Random Element Asymptotic Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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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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