Moderate deviations for stationary sequences of bounded random variables
نویسنده
چکیده
In this paper we are concerned with the moderate deviation principle for the normalized partial sums process Wn, considered as an element of D([0, 1]) (functions on [0, 1] with left-hand limits and continuous from the right), equipped with the Skorohod topology (see Section 14 in Billingsley (1968) for the description of the topology on D([0, 1])). More exactly, we say that the family of random variables {Wn, n > 0} satisfies the Moderate Deviation Principle (MDP) in D[0, 1] with speed an → 0 and good rate function I(.), if the level sets {x, I(x) ≤ α} are compact for all α < ∞, and for all Borel sets − inf t∈Γ0 I(t) ≤ lim inf n an logP( √ anWn ∈ Γ) ≤ lim sup n an logP( √ anWn ∈ Γ) ≤ − inf t∈Γ̄ I(t) . (1)
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