
05519518
j
2012a.00670
Goldstein, Larry
A probabilistic proof of the LindebergFeller central limit theorem.
Am. Math. Mon. 116, No. 1, 4560 (2009).
2009
Mathematical Association of America (MAA), Washington, DC
EN
K55
LindebergFeller central limit theorem
probabilistic proof
Stein's characterization of normal distribution
zero bias transformation
doi:10.4169/193009709X469788
The author presents a simple and easily interpretable probabilistic formulation of the Lindeberg condition and demonstrates its sufficiency and partial necessity in the Central Limit Theorem (CTL) using elementary means. The proof is based on the socalled zero bias transformation, which is motivated by Stein's characterization of the mean zero normal distribution with variance $\sigma^2$.
Wies{\l}aw Dziubdziela (Kielce)