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The purpose of this paper is the proof of an almost sure central limit theorem for subsequences. We obtain an almost sure convergence limit theorem for independent nonidentically distributed random variables. The presented results extend,to nonidentically distributed random variables, theorems given by Schatte [13].
Czasopismo
Rocznik
Tom
Strony
241--249
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
autor
- Institute of Mathematics, Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland
autor
- Institute of Mathematics, Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland
Bibliografia
- [1] M. Atlagh, Théorème central limite presque sûr et loi du logarithme itéré pour des sommes de variables aléatoires indépendantes, C. R. Acad. Sci. Paris, Sér. I, Probability Theory, 316 (1993), pp. 929-933.
- [2] P. Billingsley, Convergence of Probability Measures, Wiley, New York 1968.
- [3] G. A. Brosamler, An almost everywhere central limit theorem, Math. Proc. Cambridge Philos. Soc. 104 (1988), pp. 561-574.
- [4] M. Csörgő and L. Horváth, Invariance principles for logarithmic averages, Math. Proc. Cambridge Philos. Soc. 112 (1992), pp. 195-205.
- [5] R. M. Dudley, Real Analysis and Probability, Wadsworth, Belmont, CA, 1989.
- [6] I. Fazekas and Z. Rychlik, Almost sure functional limit theorem, Ann. Univ. Mariae Curie-Skłodowska, Lublin-Polonia, Sectio A, Vol. LVI, 7 (2002), pp. 41-58.
- [7] M. T. Lacey and W. Philipp, A note on the almost sure central limit theorem, Statist. Probab. Lett. 9 (1990), pp. 201-205.
- [8] Yu. V. Prokhorov, Convergence of random processes and limit theorems in probability theory, Teor. Veroyatnost. i Primenen. 1 (1956), pp. 177-238; English translation in: Theory Probab. Appl. 1 (1956), pp. 157-214.
- [9] B. Rodzik and Z. Rychlik, An almost sure central limit theorem for independent random variables, Ann. Inst. H. Poincaré 30 (1994), pp. 1-11.
- [10] B. Rodzik and Z. Rychlik, On the central limit theorem for independent random variables with almost sure convergence, Probab. Math. Statist. 16 (1996), pp. 299-309.
- [11] Z. Rychlik and K. S. Szuster, On strong versions of the central limit theorem, Statist. Probab. Lett. 61 (2003), pp. 348-357.
- [12] P. Schatte, On strong versions of the central limit theorem, Math. Nachr. 137 (1988), pp. 249-256.
- [13] P. Schatte, On the central limit theorem with almost sure convergence, Probab. Math. Statist. 11 (1991), pp. 315-343.
- [14] P. Schatte, Two remarks on the almost sure central limit theorem, Math. Nachr. 154 (1991), pp. 225-229.
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Bibliografia
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