On the rate of convergence of Lp norms in the CLT for Poisson random sum
Articles
Jonas Kazys Sunklodas
Institute of Mathematics and Informatics
Published 2009-12-20
https://doi.org/10.15388/LMR.2009.79
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Keywords

central limit theorem
Lp norms
Poisson random sum

How to Cite

Sunklodas, J.K. (2009) “On the rate of convergence of Lp norms in the CLT for Poisson random sum”, Lietuvos matematikos rinkinys, 50(proc. LMS), pp. 437–442. doi:10.15388/LMR.2009.79.

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)/DS, where SNλ = X1 + ··· + Xis the random sum of independent identically distributed random variables X, X1, X2, . . . with  β2+δ = E|X|2+δ < ∞ where 0 < δ \leq 1, Nλ is a random variable distributed by the Poisson distribution with the parameter λ > 0, and Nλ is independent of X1, X2, . . ..

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