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Strong invariance principles for arrays. (English) Zbl 0968.60028

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.

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)
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