Prokhorov–Loève strong law of large numbers for martingales normalized by operators
Authors:
V. V. Buldygin and V. O. Koval’
Translated by:
Oleg Klesov
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
Full-text PDF Free Access
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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.
References
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References
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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
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