caa a22 4500 475741080 CHVBK 20180406123459.0 cr unu---uuuuu 170329e20001001xx s 000 0 eng 10.1007/BF02676723 doi (NATIONALLICENCE)springer-10.1007/BF02676723 Vronskii M. M. V. Lomonosov Moscow State University, Moscow, USSR aut Refinement of the almost sure central limit theorem for associated processes [Elektronische Daten] [M. Vronskii] In this paper, for the partial sumsS n of a stationary associated random process it is proved that the logarithmic averages $$(\log n)^{ - 1} \sum\nolimits_{j = 1}^n {f(S_j /\sqrt j )/j} $$ converge almost surely. The asymptotic normality of the normalized difference between the logarithmic averages and their limiting value is established. Kluwer Academic/Plenum Publishers, 2000 associated random variables nationallicence central limit theorem nationallicence almost sure versions of limit theorems nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/4(2000-10-01), 444-451 0001-4346 68:4<444 2000 68 11006 https://doi.org/10.1007/BF02676723 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02676723 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Vronskii M. M. V. Lomonosov Moscow State University, Moscow, USSR aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/4(2000-10-01), 444-451 0001-4346 68:4<444 2000 68 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer