Independent linear forms on the group $\Omega_p$
| Autor: | Myronyuk, Margaryta |
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| Rok vydání: | 2017 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $\Omega_p$ be the group of $p$-adic numbers, $ \xi_1$, $\xi_2$, $\xi_3$ be independent random variables with values in $\Omega_p$ and distributions $\mu_1$, $\mu_2$, $\mu_3$. Let $\alpha_j, \beta_j, \gamma_j$ be topological automorphisms of $\Omega_p$. We consider linear forms $L_1 = \alpha_1\xi_1 + \alpha_2 \xi_2+\alpha_3 \xi_3$, $L_2=\beta_1\xi_1 + \beta_2 \xi_2+ \beta_3 \xi_3$ and $L_3=\gamma_1\xi_1 + \gamma_2 \xi_2+ \gamma_3 \xi_3$. Assuming that the linear forms $L_1$, $L_2$ and $L_3$ are independent, we describe possible distributions $\mu_1$, $\mu_2$, $\mu_3$. This theorem is an analogue of the well-known Skitovich-Darmois theorem, where a Gaussian distribution on the real line is characterized by the independence of two linear forms. Comment: arXiv admin note: text overlap with arXiv:1307.8284 by other authors |
| Databáze: | arXiv |
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