Abstract
We present the upper and lower bounds of the L p norms Δnp of order n -1 for all p, 1 ≤ p ≤∞, in the central limit theorem for independent identically distributed random variables with the finite fourth and zero first and third moments of summands. The proof of the upper estimates of the norms Δnp is based on a linear differential equation formed from the characteristic function of the sum of independent random variables.
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Sunklodas, J. On the Rate of Convergence of Lp Norms in the Central Limit Theorem for Independent Random Variables. Lithuanian Mathematical Journal 42, 296–307 (2002). https://doi.org/10.1023/A:1020278010643
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DOI: https://doi.org/10.1023/A:1020278010643