Asymptotic properties of the norm of extremum values of normal random elements in the space C[0, 1]期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

首页 | 本学科首页

官方微博 | 高级检索

按检索

Asymptotic properties of the norm of extremum values of normal random elements in the space C[0, 1]

Authors:

I K Matsak

Institution:

(1) Ukrainian State Academy of Light Industry, Kiev

Abstract:

We prove that

$\mathop {\lim }\limits_{n \to \infty } \left( {\left\| {Z_n } \right\| - (2 ln (n))^{1/2} \left\| \sigma \right\|} \right) = 0 a.s.,$

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 $Z_n = \mathop {\max }\limits_{l \leqslant k \leqslant n} X_k$ . Under additional restrictions on the random element X, this equality can be strengthened. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 9, pp. 1227–1235, September, 1998.

Keywords:

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏