On the law of the iterated logarithm for weighted sums of independent random variables in a Banach space. (English. Ukrainian original) Zbl 0810.60033
Ukr. Math. J. 45, No. 9, 1372-1381 (1993); translation from Ukr. Mat. Zh. 45, No. 9, 1225-1231 (1993).
Summary: Assume that \((X_ n)\) are independent random variables in a Banach space, \((b_ n)\) is a sequence of real numbers, \(S_ n = \sum^ n_ 1 b_ iX_ i\), and \(B_ n = \sum^ n_ 1 b^ 2_ i\). Under certain moment restrictions imposed on the variables \(X_ n\), the conditions for the growth of the sequence \((b_ n)\) are established, which are sufficient for the almost sure boundedness and precompactness of the sequence \((S_ n/(B_ n \ln \ln B_ n)^{1/2})\).
MSC:
| 60F15 | Strong limit theorems |
| 60B12 | Limit theorems for vector-valued random variables (infinite-dimensional case) |
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