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2014
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info:eu-repo/semantics/altIdentifier/urn/urn:nbn:ch:serval-BIB_D3B8D9C954A21
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Chance variables Stochastic variables Groups, Lie Numbers, Large Large numbers, Law ofCiter ce document
D. Neuenschwander, « On Chung's Law of Large Numbers on Simply Connected Step 2-Nilpotent Lie Groups », Serveur académique Lausannois, ID : 10.1007/s10958-013-1638-5
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Ord´o~nez Cabrera and Sung (2002) have proved that under certain "moment" conditions, for triangular arrays of weighted Banach-valued random variables, a.s. convergence, convergence in L1, convergence in probability, and complete convergence to 0 are equivalent, thus giving a variant of Chung's law of large numbers. We extend their result (under slightly sharper technical conditions) to symmetric random variables on simply connected step 2-nilpotent Lie groups.