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Zapiski Nauchnykh Seminarov LOMI, 1982, Volume 119, Pages 7–13
(Mi znsl3981)
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This article is cited in 1 scientific paper (total in 1 paper)
Moderate deviations for densities in $\mathbb R^k$
N. N. Amosova, W. Richter
Abstract:
Let $\{X^i=(X^i_1,\dots,X^i_k),\, i=1,2,\dots\}$ be a sum of independent identically distributed random vectors in $\mathbb R^k$, let $\varphi_{0,E}$ be a density of standard normal distribution in $\mathbb R^k$ and let $p_n(x)$ be a density of $z_n=\frac{1}{\sqrt n}S_n$. Conditions upon distribution of $X^1$ are given under which
$$
p_n(x)=\varphi_{0,E}(x)(1+o(1)),\quad n\to\infty
$$
uniformly in $x$, $x\in\mathcal A_n$, and $\mathcal A_n=\{x\in\mathbb R^k:|x|\leqslant c\sqrt{\log n}\}, c>0$.
Citation:
N. N. Amosova, W. Richter, “Moderate deviations for densities in $\mathbb R^k$”, Problems of the theory of probability distributions. Part VII, Zap. Nauchn. Sem. LOMI, 119, "Nauka", Leningrad. Otdel., Leningrad, 1982, 7–13
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https://www.mathnet.ru/eng/znsl3981 https://www.mathnet.ru/eng/znsl/v119/p7
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