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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1966, Volume 11, Issue 1, Pages 129–140 (Mi tvp572)

Short Communications

On the speed of convergence in the local limit theorem for lattice distributions

N. G. Gamkrelidze

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: The paper deals with the speed of convergence in the local limit theorem for lattice distributions. Numerical calculations have been carried out for the example of random variables taking on values $-3$, 0, 7 with probability $1/3$ each. It follows as a result of these calculations that the behaviour of the probabilities $P_n(k)$ is much less regular than one might have expected. Their “smoothing” which should take place according to the local limit theorem occurs when $n$ is very large.
An estimate of the number of summands necessary to achieve the prescribed accuracy of the normal approximation to $P_n(k)$ is also given.

Full text: PDF file (593 kB)

English version:
Theory of Probability and its Applications, 1966, 11:1, 114–125

Bibliographic databases:

Citation: N. G. Gamkrelidze, “On the speed of convergence in the local limit theorem for lattice distributions”, Teor. Veroyatnost. i Primenen., 11:1 (1966), 129–140; Theory Probab. Appl., 11:1 (1966), 114–125

Citation in format AMSBIB
\Bibitem{Gam66} \by N.~G.~Gamkrelidze \paper On the speed of convergence in the local limit theorem for lattice distributions \jour Teor. Veroyatnost. i Primenen. \yr 1966 \vol 11 \issue 1 \pages 129--140 \mathnet{http://mi.mathnet.ru/tvp572} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=198526} \zmath{https://zbmath.org/?q=an:0168.39003} \transl \jour Theory Probab. Appl. \yr 1966 \vol 11 \issue 1 \pages 114--125 \crossref{https://doi.org/10.1137/1111007}