A conditional strong large deviation result and a functional central limit theorem for the rate function

Abstract

We study the large deviation behaviour of $S_n={\sum }_{j=1}^n{W}_j{Z}_j$, where $(W_j{)}_{j\in \mathbb{N}}$ and $(Z_j{)}_{j\in \mathbb{N}}$ are sequences of real-valued, independent and identically distributed random variables satisfying certain moment conditions, independent of each other. More precisely, we prove a conditional strong large deviation result and describe the fluctuations of the random rate function through a functional central limit theorem.

17 pages; added references (by Dembo and Kontoyiannis)

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