Abstract
The aim of this paper is to provide an alternative approach to the classical theory ofsums of independent random variables. It shows that the Kolmogorov inequalities may be avoided in the proof of thethree series theorem, and theequivalence lemma follows from a very simple argument. The main idea is to relate the a. s. convergence of a series to the fact that their paths remain bounded.
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Vélez, R. A new approach to series of independent random variables. Test 10, 405–418 (2001). https://doi.org/10.1007/BF02595705
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DOI: https://doi.org/10.1007/BF02595705