A complete convergence theorem for row sums from arrays of rowwise independent random elements in Rademacher type \(p\) Banach spaces. (English) Zbl 1237.60022

Summary: We extend in several directions a complete convergence theorem for row sums from an array of row-wise independent random variables obtained by S. H. Sung, A. I. Volodin and T.-C. Hu [Stat. Probab. Lett. 71, No. 4, 303–311 (2005; Zbl 1087.60030)] to an array of row-wise independent random elements taking values in a real separable Rademacher type \(p\) Banach space. An example is presented which illustrates that our result extends the result in [loc. cit.] even for the random variable case.


60F15 Strong limit theorems
60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
60B11 Probability theory on linear topological spaces


Zbl 1087.60030
Full Text: DOI


[1] DOI: 10.1073/pnas.33.2.25 · Zbl 0030.20101
[2] DOI: 10.1214/aoms/1177730037 · Zbl 0033.29001
[3] DOI: 10.1080/07362999908809645 · Zbl 0940.60032
[4] Taylor , R.L. ( 1978 ).Stochastic Convergence of Weighted Sums of Random Elements in Linear Spaces.Lecture Notes in Mathematics, Vol. 672. Springer-Verlag, Berlin. · Zbl 0443.60004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.