20.500.12556/RUL-22457 Optimal averaging procedures in almost sure central limit theory Let X1,X2, . . . be i.i.d. random variables with EX1 = 0,EX2 1 = 1, Sn = X1 +.. .+Xn and let (dk) be a positive numerical sequence. We investigate the a.s. convergence of the averages 1 DN N Xk=1 dkI{Sk/¡Ìk ¡Ü x} ,where DN = PN k=1 dk. In the case of dk = 1/k we have logarithmic means and by the almost sure central limit theorem the above averages converge a.s. (x), the standard normal distribution function. It is also known that the analogous convergence relation fails for dk = 1 (ordinary averages). In this paper we give a fairly complete solution of the problem for which weight sequences the above convergence relation and its refinements hold. true false false Angleški jezik Neznan jezik Delo ni kategorizirano 2014-07-11 14:26:41 2014-07-11 14:26:41 2022-06-02 03:50:32 0000-00-00 00:00:00 2005 0 0 Str. 271-282 no. 2 Vol. 2 2005 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 311 1854-0023 24318301 http://mrvar.fdv.uni-lj.si/pub/mz/mz2.1/hoerman.pdf 1 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=22457 Fakulteta za družbene vede Metodološki zvezki 0 0 0