The Stein-Tikhomirov method and a nonclassical central limit theorem

Mathematical Notes

Volumn 71, Issue 3-4, 2002, Pages 550-555

  Formanov, Sh K ^a  

^a S YU YUNUSOV INSTITUTE OF THE CHEMISTRY OF PLANT SUBSTANCES   (Uzbekistan)

Author keywords

Bernoulli random variables; Central limit theorem; Class of twice differentiable characteristic functions; Distribution function; Stein Tikhomirov method

Indexed keywords

EID: 0141848541     PISSN: 00014346     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1014840017098     Document Type: Article

References (5)

1. Ch. Stein, "A bound for error in the normal approximation to the distribution of a sum of dependent random variables," Proc. 6th Berkley Symp. Math. Stat. and Prob., 2 (1972), 583-602.
2. A. N. Tikhomirov, "On the convergence of the remainder in the central limit theorem for weakly dependent random variables" Teor. Veroyatnost. i Primenen. [Theory Probab. Appl.], 25 (1980), no. 4, 800-818.
3. Yu. I. Linnik and I. V. Ostrovskii, Expansions of Random Variables and Vectors [in Russian], Nauka, Moscow, 1972.
4. V. I. Rotar', "On the generalization of the Lindeberg-Feller theorem," Mat. Zametki [Math. Notes], 18 (1975), no. 1, 129-135.
5. R. Sh. Liptser and A. N. Shiryaev, Martingale Theory [in Russian], Nauka, Moscow, 1986.