Displaying similar documents to “A penalized bandit algorithm.”

A central limit theorem for processes generated by a family of transformations

Marian Jabłoński

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Let τ n , n 0 be a sequence of measure preserving transformations of a probability space (Ω,Σ,P) into itself and let f n , n 0 be a sequence of elements of L 2 ( Ω , Σ , P ) with E f n = 0 . It is shown that the distribution of ( i = 0 n f i τ i . . . τ 0 ) ( D ( i = 0 n f i τ i . . . τ 0 ) ) - 1 tends to the normal distribution N(0,1) as n → ∞. 1985 Mathematics Subject Classification: 58F11, 60F05, 28D99.