Li, Deli; Huang, Mei Ling; Rosalsky, Andrew Strong invariance principles for arrays. (English) Zbl 0968.60028 Bull. Inst. Math., Acad. Sin. 28, No. 3, 167-181 (2000). A strong approximation theorem, a strong invariance theorem and a generalized functional law of the iterated logarithm (LIL) are established for polygonal processes defined by row-sums of an i.i.d. array of random variables. These results are used to prove a Strassen-type functional LIL and to derive rates of convergence for moderate deviations of a polygonal process based on sums of an i.i.d. sequence. Banach space versions of the results are presented. The well-known Komlós-Major-Tusnády strong approximations are the key tools in the proofs. Reviewer: R.James Tomkins (Regina) Cited in 2 Documents MSC: 60F15 Strong limit theorems 60F17 Functional limit theorems; invariance principles 60F10 Large deviations 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case) Keywords:i.i.d. array of random variables; functional law of the iterated logarithm; strong invariance principles; strong approximation principles; polygonal process; Wiener process PDFBibTeX XMLCite \textit{D. Li} et al., Bull. Inst. Math., Acad. Sin. 28, No. 3, 167--181 (2000; Zbl 0968.60028)