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Teoriya Veroyatnostei i ee Primeneniya, 1974, Volume 19, Issue 1, Pages 84–103
(Mi tvp2760)
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This article is cited in 6 scientific papers (total in 6 papers)
Limit theorems for compositions of distributions on some nilpotent Lie groups
A. D. Vircer Moscow
Abstract:
Let $X_1,X_2,\dots$ be a sequence of independent random elements of unipotent group $G$ (upper triangular matrices with 1's on the diagonal) with the same distribution $\mu$ on $G$. Asymptotical behaviour of the distribution $\mu^n$ of the product $X(n)=X_1X_2\dots X_n$ is studied.
It is shown that the distribution of the properly normalized product $X(n)$ weakly converges to the distribution of $Z(1)$, where $Z(t)$ is an invariant Brownian motion on some nilpotent Lie group $G_\mu$ with the same space as that of $G$ and the multiplication rule dependent on the measure $\mu$. Necessary and sufficient conditions are obtained for the two compositions $\mu_1^n$ and $\mu_2^n$ to come together as $n\to\infty$.
Received: 22.01.1973
Citation:
A. D. Vircer, “Limit theorems for compositions of distributions on some nilpotent Lie groups”, Teor. Veroyatnost. i Primenen., 19:1 (1974), 84–103; Theory Probab. Appl., 19:1 (1974), 86–105
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Abstract page: | 139 | Full-text PDF : | 58 |
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