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Teoriya Veroyatnostei i ee Primeneniya, 1973, Volume 18, Issue 2, Pages 396–402
(Mi tvp4305)
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This article is cited in 7 scientific papers (total in 7 papers)
Short Communications
On a Multidimensional Version of the Kolmogorov Uniform Limit Theorem
E. L. Presman Moscow
Abstract:
It is proved, that, for any $k$, there exist such a constant $c(k)$, that for any distribution function $F=F(x)$ in $R^k$, one can find a sequence of the vectors $\{a_n\}$ for which
$$
\rho (F^n, E_{-na_{n}}\exp n (E_{a_n}F - E))<c(k)n^{-1/3}
$$
where $\rho (F,g)=\sup_x |F(x)-G(x)|$, $F^n$ is the $n$-time convolution of $F$ with itself and $E_a$ is the distribution function corresponding to the unit mass at $a$.
Received: 18.05.1971
Citation:
E. L. Presman, “On a Multidimensional Version of the Kolmogorov Uniform Limit Theorem”, Teor. Veroyatnost. i Primenen., 18:2 (1973), 396–402; Theory Probab. Appl., 18:2 (1973), 378–384
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Abstract page: | 208 | Full-text PDF : | 90 |
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