Birkel, Thomas A note on the strong law of large numbers for positively dependent random variables. (English) Zbl 0661.60048 Stat. Probab. Lett. 7, No. 1, 17-20 (1988). The author presents strong laws of large numbers for sequences of random variables which are either pairwise quadrant dependent or associated. The theorems presented give extensions of Kolmogorov’s classical strong law to positively dependent random variables. Reviewer: Z.Rychlik Cited in 5 ReviewsCited in 40 Documents MSC: 60F15 Strong limit theorems Keywords:associated random variables; strong laws of large numbers; positively dependent random variables PDF BibTeX XML Cite \textit{T. Birkel}, Stat. Probab. Lett. 7, No. 1, 17--20 (1988; Zbl 0661.60048) Full Text: DOI References: [1] Block, H.W.; Ting, M.L., Some concepts of multivariate dependence, Comm. statist. A, 10, 8, 749-762, (1981) · Zbl 0478.62045 [2] Csörgő, S.; Tandori, K.; Totik, V., On the strong law of large numbers for pairwise independent random variables, Acta math. hung., 42, 319-330, (1983) · Zbl 0534.60028 [3] Esary, J.; Proschan, F.; Walkup, D., Association of random variables with applications, Ann. math. statist., 38, 1466-1474, (1967) · Zbl 0183.21502 [4] Etemadi, N., Stability of sums of weighted nonnegative random variables, J. multivariate anal., 13, 361-365, (1983) · Zbl 0531.60034 [5] Karlin, S.; Rinott, Y., Classes of orderings of measures and related correlation inequalities. I. multivariate totally positive distributions, J. multivariate anal., 10, 467-498, (1980) · Zbl 0469.60006 [6] Lehmann, E.L., Some concepts of dependence, Ann. math. statist., 37, 1137-1153, (1966) · Zbl 0146.40601 [7] Newman, C.M., Asymptotic independence and limit theorems for positively and negatively dependent random variables, (), 127-140 [8] Newman, C.M.; Wright, A.L., Associated random variables and martingale inequalities, Z. wahrsch. verw. geb., 59, 361-371, (1982) · Zbl 0465.60010 [9] Shaked, M., A general theory of some positive dependence notions, J. multivariate anal., 12, 199-218, (1982) · Zbl 0486.62021 [10] Wood, T.E., Sample paths of demimartingales, (), 365-373 · Zbl 0545.60052 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.