Theory of Probability and Mathematical Statistics

Prokhorov-Loève strong law of large numbers for martingales normalized by operators

Author(s): V. V. Buldygin; V. O. Koval'
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, vipusk 73 (2005).
Journal: Theor. Probability and Math. Statist. No. 73 (2006), 31-46.
MSC (2000): Primary 60F15
Posted: January 17, 2007
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Abstract: We study strong laws of large numbers for multivariate martingales normalized by linear operators in a finite-dimensional Euclidean space. Corollaries of the general results are considered for martingales under moment restrictions.

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Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 60F15

V. V. Buldygin
Affiliation: National Technical University of Ukraine ``KPI'', Department of Mathematical Analysis and Probability Theory, Pr. Peremogy 37, 03056 Kyiv--56, Ukraine
Email: valbuld@comsys.ntu-kpi.kiev.ua

V. O. Koval'
Affiliation: Zhytomyr State University for Technology, Department of Mathematics, Chernyakhovskii Street 103, 10005 Zhytomyr, Ukraine
Email: vkoval@com.zt.ua

DOI: 10.1090/S0094-9000-07-00679-5
PII: S 0094-9000(07)00679-5
Keywords: Strong law of large numbers, almost sure convergence, almost sure boundedness, martingales, normalizations by operators
Received by editor(s): 23/FEB/2005
Posted: January 17, 2007
Copyright of article: Copyright 2007, American Mathematical Society

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