On the rate of convergence of Lp norms in the CLT for Poisson random sum - Sunklodas, Jonas Kazys (Lietuvos matematikos rinkinys, 2009)
In the paper, we present the upper bound of Lp norm δλ,p of the order λ-δ/2 for all 1 ≤ p ≤ ∞, in the central limit theorem for a standardized random sum (SNλ - ESNλ)/DSNλ , where SNλ = X1 + ··· + XNλ is the random sum of independent identically distributed random variables X, X1, X2, . . . with β2+δ = E|X|2+δ < ∞ where 0 < δ ≤ 1, Nλ is a random variable distributed by the Poisson distribution with the parameter λ > 0, and Nλ is independent of X1, X2, . . ..