Three Elementary Proofs of the Central Limit Theorem with Applications to Random Sums
T. Cacoullos, Nickos Papadatos, V. Papathanasiou · Birkhäuser Boston eBooks · 1998
Three simple proofs of the classical CLT are presented. The proofs are based on some basic properties of covariance kernels or ω-functions in conjunction with bounds for the total variation distance. Applications to random sum CLT’s are also given.