Asymptotic expansion in approximation by normal law

Algimantas  Bikelis; Juozas  Augutis; Kazimieras  Padvelskis

doi:10.15388/LMR.2011.tt01

Articles

Algimantas Bikelis

Vytautas Magnus University

Juozas Augutis

Vytautas Magnus University

Kazimieras Padvelskis

Vytautas Magnus University

Published 2011-12-15

https://doi.org/10.15388/LMR.2011.tt01

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Keywords

probability distributions in R^k,
convolutions
Bergström identity
Appell polynomials
Chebyshev–Cramer asymptotic expansion

How to Cite

Bikelis, A., Augutis, J. and Padvelskis, K. (2011) “Asymptotic expansion in approximation by normal law”, Lietuvos matematikos rinkinys, 52(proc. LMS), pp. 349–352. doi:10.15388/LMR.2011.tt01.

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Abstract

We consider the asymptotic behavior of the convolution P^*n(A\sqrt{n}) of a k-dimensional probability distribution P(A) as n \to \infty for A from the \sigma-algebra M of Borel subsets of Euclidian space R^k or from its subclasses.

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