Geodesic
Almost sure central limit theorem without logarithmic sums
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 8, Tome 320 (2004), pp. 110-119
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We investigate possible rates of convergence in almost sure CLT for sums of independent random variables and martingales. 
@article{ZNSL_2004_320_a8,
     author = {A. I. Martikainen},
     title = {Almost sure central limit theorem without logarithmic sums},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {110--119},
     year = {2004},
     volume = {320},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_320_a8/}
}
TY  - JOUR
AU  - A. I. Martikainen
TI  - Almost sure central limit theorem without logarithmic sums
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2004
SP  - 110
EP  - 119
VL  - 320
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2004_320_a8/
LA  - ru
ID  - ZNSL_2004_320_a8
ER  - 
%0 Journal Article
%A A. I. Martikainen
%T Almost sure central limit theorem without logarithmic sums
%J Zapiski Nauchnykh Seminarov POMI
%D 2004
%P 110-119
%V 320
%U http://geodesic.mathdoc.fr/item/ZNSL_2004_320_a8/
%G ru
%F ZNSL_2004_320_a8
A. I. Martikainen. Almost sure central limit theorem without logarithmic sums. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 8, Tome 320 (2004), pp. 110-119. http://geodesic.mathdoc.fr/item/ZNSL_2004_320_a8/

[1] V. V. Petrov, Summy nezavisimykh sluchainykh velichin, M., 1972 | MR

[2] A. I. Martikainen, “Ob usilennom zakone bolshikh chisel dlya upravlyaemykh summ”, Vestnik LGU, 1977, no. 1, 56–65 | MR | Zbl

[3] G. A. Brosamler, “An almost everywhere central limit theorem”, Math. Proc. Cambridge Philos. Soc., 104 (1988), 561–574 | DOI | MR | Zbl

[4] P. Schatte, “On the central limit theorem with almost sure convergence”, Math. Nachr., 137 (1988), 249–256 | DOI | MR | Zbl

[5] U. Einmahl, D. M. Mason, “Darling–Erdös theorems for martingales”, J. Theor. Probab., 2 (1989), 437–460 | DOI | MR | Zbl

[6] M. Atlagh, “Théorème central limite prescue sûr et loi du logarithme itéré pour des sommes de variables aléatoires indépendantes”, C. R. Acad. Paris, Sér. I, 316 (1993), 929–933 | MR | Zbl

[7] I. Berkes, H. Dehling, “Some limit theorems in log density”, Ann. Probab., 21 (1993), 1640–1670 | DOI | MR | Zbl

[8] I. Berkes, E. Csáki, “A universal result in almost sure central limit theorem”, Stoch. Proc. Appl., 94 (2001), 105–134 | DOI | MR | Zbl

[9] A. I. Martikainen, “On rate of convergence in almost sure central limit theorem”, Teor. Veroyatn. Mat. Statist., 66 (2002), 77–81 | MR