References
T. K. Chandra, “Uniform integrability in the Cesàro sense and the weak law of large numbers,” Sankhya, Ser. A, 51, 309–317 (1989).
A. Gut, “The weak law of large numbers for arrays,” Statist. Probab. Lett., 14, 49–52 (1992).
J. Hoffmann-Jorgensen and G. Pisier, “The law of large numbers and the central limit theorem in Banach spaces,” Ann. Probab., 4, 587–599 (1976).
T. C. Hu, M. Ordóñez Cabrera, and A. I. Volodin, “Convergence of randomly weighted sums of Banach space valued random elements and uniform integrability concerning the random weights,” Statist. Probab. Lett., 51, 155–164 (2001).
J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces. I, Springer, Berlin (1977).
M. Ordóñez Cabrera, “Convergence of weighted sums of random variables and uniform integrability concerning the weights,” Collect. Math., 45, 121–132 (1994).
M. Ordóñez Cabrera, “Convergence in mean of weighted sums of a nk -compactly uniformly integrable random elements in Banach spaces,” Intern. J. Math. Math. Sci., 20, 443–450 (1997).
M. Ordóñez Cabrera and A. I. Volodin, “On conditional compactly uniform pth-order integrability of random elements in Banach spaces,” Statist. Probab. Lett., 55, 301–309 (2001).
V. K. Rohatgi, “Convergence of weighted sums of independent random variables,” Proc. Cambridge Philos. Soc., 69, 305–307 (1971).
A. Rosalsky and M. Sreehari, “On the limiting behavior of randomly weighted partial sums,” Statist. Probab. Lett., 40, 403–410 (1998).
S. J. Szarek, “A Banach space without a basis which has the bounded approximation property,” Acta Math., 159, Nos. 1–2, 81–98 (1987).
X. C. Wang and M. B. Rao, “A note on convergence of weighted sums of random variables,” Intern. J. Math. Math. Sci., 8, 805–812 (1985).
X. C. Wang and M. B. Rao, “Some results on the convergence of weighted sums of random elements in separable Banach spaces,” Stud. Math., 86, 131–153 (1987).
Author information
Authors and Affiliations
Additional information
The research of M. Ordóñez Cabrera has been partially supported by DGES(grant No. BFM 2000-0344-C02-01) and Junta de Andalucia (grant No. FQM 127).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Pamplona, Spain, 2003, Part III.
Rights and permissions
About this article
Cite this article
Ordóñez Cabrera, M., Volodin, A. Convergence of randomly weighted sums of Banach-space-valued random elements under some conditions of uniform integrability. J Math Sci 138, 5450–5459 (2006). https://doi.org/10.1007/s10958-006-0311-7
Issue Date:
DOI: https://doi.org/10.1007/s10958-006-0311-7