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 Sibirsk. Mat. Zh., 2003, Volume 44, Number 6, Pages 1407–1424 (Mi smj1266)

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

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

Bibliographic databases:

UDC: 519.21

Citation: O. Sh. Sharipov, “The law of the iterated logarithm for weakly dependent Hilbert space valued random variables”, Sibirsk. Mat. Zh., 44:6 (2003), 1407–1424; Siberian Math. J., 44:6 (2003), 1111–1126

Citation in format AMSBIB
\Bibitem{Sha03} \by O.~Sh.~Sharipov \paper The law of the iterated logarithm for weakly dependent Hilbert space valued random variables \jour Sibirsk. Mat. Zh. \yr 2003 \vol 44 \issue 6 \pages 1407--1424 \mathnet{http://mi.mathnet.ru/smj1266} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2034946} \zmath{https://zbmath.org/?q=an:1046.60023} \transl \jour Siberian Math. J. \yr 2003 \vol 44 \issue 6 \pages 1111--1126 \crossref{https://doi.org/10.1023/B:SIMJ.0000007487.22414.15} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000187464000019} 

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This publication is cited in the following articles:
1. O. Sh. Sharipov, “The bounded law of the iterated logarithm for weakly dependent random variables with values in a type 2 Banach space”, Theory Probab. Appl., 49:3 (2005), 444–457
2. Sharipov O.Sh., “Laws of the iterated logarithm and an almost sure invariance principle for mixing B–valued random variables and autoregressive processes”, Lithuanian Mathematical Journal, 49:2 (2009), 203–215
3. Fu K.-A., “LIL behavior for weakly dependent random variables in Banach spaces”, Acta Math Hungar, 128:4 (2010), 315–327
4. Fu KeAng, Zhang LiXin, “LIL behavior for B-valued strong mixing random variables”, Science China-Mathematics, 54:4 (2011), 785–792
5. Fu K.-A., “A general LIL for B-valued geometrically weighted series under dependent assumption”, Acta Math Hungar, 133:4 (2011), 311–323
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