A Non-Elementary Proof by Differential Equation for the Central Limit Theorem (original) (raw)

2013

Abstract

The proofs of the central limit theorem are divided into two categories: elementary and non-elementary. Proofs using the characteristic function are called non-elementary while the other proofs are called elementary. Using differential equation, this paper gives a new non-elementary proof for the central limit theorem. This proof is based on a differential equation and does not use second order Taylor expansion of any characteristic function. It is apparent that given proof may only have a pedagogical importance.

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