This article is cited in 5 papers

The law of the iterated logarithm for weakly dependent Hilbert space valued random variables

O. Sh. Sharipov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: We consider the bounded and compact laws of the iterated logarithm for weakly dependent Hilbert space valued random variables. Under optimal moment conditions, we prove the bounded and compact laws of the iterated logarithm for sequences of identically distributed Hilbert space valued random variables satisfying the uniform strong mixing condition.

Keywords: law of the iterated logarithm, Hilbert space valued random variable, mixing condition.

UDC: 519.21

Received: 04.01.2003

 English version: Siberian Mathematical Journal, 2003, 44:6, 1111–1126

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