Lietuvos Matematikos Rinkinys (Dec 2009)
On the rate of convergence of Lp norms in the CLT for Poisson random sum
Abstract
In the paper, we present the upper bound of Lp norm \deltaλ,p of the order λ-δ/2 for all 1 \leq p \leq ∞, 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 0, and Nλ is independent of X1, X2, . . ..
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