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Teoriya Veroyatnostei i ee Primeneniya, 1975, Volume 20, Issue 1, Pages 40–57
(Mi tvp2987)
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This article is cited in 3 scientific papers (total in 3 papers)
Multidimensional limit theorems for large deviations
L. V. Osipov Leningrad State University
Abstract:
Let $S_n=X^{(1)}+\dots+X^{(n)}$ be a sum of independent identically distributed random vectors in $R^k$ and let $\Phi$ be the standard normal distribution in $R^k$. Conditions upon distribution of $X^{(1)}$ are given under which
$$
\mathbf P\{S_n/\sqrt n\in A_n\}=\Phi(A_n)(1+o(1)),\quad n\to\infty,
$$
uniformly in sequences of Borel sets $\{A_n\}$ such that $\Phi(A_n)\ge\Phi(x\colon|x|>\Lambda(n))$ where $\Lambda(z)\uparrow\infty$ is a function satisfying condition (8). In Theorems 1 and 2, we consider the case $\Lambda(z)=bz^\alpha$, $b>0$, $0<\alpha<1/2$.
Received: 19.04.1972
Citation:
L. V. Osipov, “Multidimensional limit theorems for large deviations”, Teor. Veroyatnost. i Primenen., 20:1 (1975), 40–57; Theory Probab. Appl., 20:1 (1975), 38–56
Linking options:
https://www.mathnet.ru/eng/tvp2987 https://www.mathnet.ru/eng/tvp/v20/i1/p40
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