Lietuvos Matematikos Rinkinys (Dec 2009)

On the rate of convergence of Lp norms in the CLT for Poisson random sum

  • Jonas Kazys Sunklodas

DOI
https://doi.org/10.15388/LMR.2009.79
Journal volume & issue
Vol. 50, no. proc. LMS

Abstract

Read online

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, . . ..

Keywords