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Teoriya Veroyatnostei i ee Primeneniya, 1974, Volume 19, Issue 1, Pages 163–168
(Mi tvp2768)
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This article is cited in 57 scientific papers (total in 57 papers)
Short Communications
On the continuity of the distribution of a sum of dependent variables connected with independent walks on the lines
A. K. Grincevičius Institute of Physics and Mathematics, Academy of Sciences Lithuanian SSR
Abstract:
Let
$
\begin{pmatrix}
\xi_j&\eta_j
\\
0&1
\end{pmatrix}
$, $j=1,2,\dots,$ be independent identically distributed random matrices and
$$
\begin{pmatrix}
\varphi_n&\psi_n
\\
0&0
\end{pmatrix}
=\prod_{j=1}^n
\begin{pmatrix}
\xi_j&\eta_j
\\
0&1
\end{pmatrix}.
$$
Then $\psi_n=\eta_1+\eta_2\xi_1+\dots+\eta_n\xi_1\dots\xi_{n-1}$. Convergence and continuity of the limit distribution of $\psi_n$ as $n\to\infty$ are studied.
Received: 10.04.1973
Citation:
A. K. Grincevičius, “On the continuity of the distribution of a sum of dependent variables connected with independent walks on the lines”, Teor. Veroyatnost. i Primenen., 19:1 (1974), 163–168; Theory Probab. Appl., 19:1 (1974), 163–168
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https://www.mathnet.ru/eng/tvp2768 https://www.mathnet.ru/eng/tvp/v19/i1/p163
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