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


Authors: V. V. Buldygin and V. O. Koval'
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 73 (2005).
Journal: Theor. Probability and Math. Statist. 73 (2006), 31-46
MSC (2000): Primary 60F15
DOI: https://doi.org/10.1090/S0094-9000-07-00679-5
Published electronically: January 17, 2007
MathSciNet review: 2213334
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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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Additional Information

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, Chernyakhovskiĭ Street 103, 10005 Zhytomyr, Ukraine
Email: vkoval@com.zt.ua

DOI: https://doi.org/10.1090/S0094-9000-07-00679-5
Keywords: Strong law of large numbers, almost sure convergence, almost sure boundedness, martingales, normalizations by operators
Received by editor(s): February 23, 2005
Published electronically: January 17, 2007
Article copyright: © Copyright 2007 American Mathematical Society

American Mathematical Society