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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2013, Volume 9, Number 4, Pages 582–593
(Mi jmag580)
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On the Skitovich–Darmois Theorem for $\mathbf{a}$-Adic Solenoids
I. P. Mazur B. Verkin Institute for Low Temperature Physics and Engineering,
National Academy of Sciences of Ukraine,
47 Lenin Ave., Kharkiv 61103, Ukraine
Abstract:
By the Skitovich–Darmois theorem, the Gaussian distribution on the real line is characterized by the independence of two linear forms of $n$ independent random variables. The theorem is known to fail for a compact connected Abelian group even in the case when $n=2$. In the paper, it is proved that a weak analogue of the Skitovich–Darmois theorem holds for some $\mathbf{a}$-adic solenoids if we consider three independent linear forms of three random variables.
Key words and phrases:
Skitovich–Darmois theorem, functional equation, $\mathbf{a}$-adic solenoid.
Received: 10.07.2013
Citation:
I. P. Mazur, “On the Skitovich–Darmois Theorem for $\mathbf{a}$-Adic Solenoids”, Zh. Mat. Fiz. Anal. Geom., 9:4 (2013), 582–593
Linking options:
https://www.mathnet.ru/eng/jmag580 https://www.mathnet.ru/eng/jmag/v9/i4/p582
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Abstract page: | 143 | Full-text PDF : | 38 | References: | 28 |
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