On C.R. RAO’s theorem for locally compact abelian groups
Keyword(s):
Let x1, x2, x3 be independent random variables with values in a locally compact Abelian group X with nonvanish- ing characteristic functions, and aj, bj be continuous endomorphisms of X satisfying some restrictions. Let L1 = a1x1 + a2x2 + a3x3, L2 = b1x1 + b2x2 + b3x3. It was proved that the distribution of the random vector (L1; L2) determines the distributions of the random variables xj up a shift. This result is a group analogue of the well-known C.R. Rao theorem. We also prove an analogue of another C.R. Rao’s theorem for independent random variables with values in an a-adic solenoid.
2010 ◽
Vol 88
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pp. 339-352
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2017 ◽
Vol 91
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pp. 949-967
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1974 ◽
Vol 10
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pp. 59-66
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2019 ◽
Vol 152
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pp. 82-88
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1994 ◽
Vol 14
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pp. 130-138
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2007 ◽
Vol 75
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pp. 369-390
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2008 ◽
Vol 340
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pp. 219-225
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