  We study the large deviation behaviour of $S_n=\sum_{j=1}^n W_jZ_j$, 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.
