Gut, Allan; Martin-Löf, Anders - In: Statistics & Probability Letters 96 (2015) C, pp. 341-345
, Feller (1945), states that Snnlog2n→p1 as n→∞. However, almost sure convergence fails, more precisely, lim supn→∞Snnlog2n …=+∞ a.s. and lim infn→∞Snnlog2n=1 a.s. as n→∞. Csörgő and Simons (1996) have shown that almost sure convergence holds for …