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MR2071429 (2005k:62183) 62L20 (91B32 91E40 93C40)
Lamberton, Damien; Pagès, Gilles; Tarrès, Pierre When can the two-armed bandit algorithm be trusted? Ann. Appl. Probab. 14 (2004), no. 3, 1424–1454.
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