On the Large Deviation Principle for the Almost Sure CLT M.A.Lifshits, E.S. Stankevich

Let Sk be the k-th partial sum of real valued i.i.d. random variables X1 , X2 , ... Define the empirical Pn measures with logarithmic weights Qn = log1 n k=1 k1 δSk /√k . If E|X1 |m < ∞ for all m > 0, then Qn satisfies strong large deviation principle, as M.Heck, P.March and T.Sepp¨alainen have recently proved. We show that the moment assumptions are optimal in this statement.

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