zbMATH — the first resource for mathematics

An invariance principle for weakly associated random vectors. (English) Zbl 0611.60028
An invariance principle for a stationary, weakly associated sequence of \({\mathbb{R}}^ d\)-valued or Hilbert space valued random elements which satisfy a covariance summability condition is proved. This paper generalizes the earlier one by C. M. Newman and A. L. Wright, Ann. Probab. 9, 671-675 (1981; Zbl 0465.60009).
Reviewer: E.Kubilius

60F17 Functional limit theorems; invariance principles
Full Text: DOI
[1] Barlow, R.E.; Proschan, F., Statistical theory of reliability and life testing probability and life testing probability models, (1975), Holt Rinehart and Winston · Zbl 0379.62080
[2] Burton, R.M.; Waymire, E., Scaling limits for associated random measures, Ann. probab., (1985), to appear · Zbl 0579.60039
[3] Esary, I.; Proschan, F.; Walkup, D., Association of random variables with applications, Ann. math. statist., 38, 1466-1474, (1967) · Zbl 0183.21502
[4] Fortuin, C.; Kastelyn, P.; Ginibre, J., Correlation inequalities on some partially ordered sets, Comm. math. phys., 22, 89-103, (1971) · Zbl 0346.06011
[5] Joag-Dev, K.; Proschan, F., Negative association of random variables with applications, Ann. statist., 11, 286-295, (1983) · Zbl 0508.62041
[6] Newman, C.M., Normal fluctuations and the FKG inequalities, Comm. math. phys., 79, 119-128, (1980) · Zbl 0429.60096
[7] Newman, C.M.; Tong, H., Asymptotic independence and limit theorems for positively and negatively dependent random variables, IMS lecture notes-monograph series, Vol. 5, 127-140, (1984)
[8] Newman, C.M.; Wright, A.L., An invariance principle for certain dependent sequences, Ann. probab., 9, 671-675, (1981) · Zbl 0465.60009
[9] Newman, C.M.; Wright, A.L., Associated random variables and martingale inequalities, Z. wahrsch. verw. geb., 59, 361-372, (1982) · Zbl 0465.60010
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.