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.
Categories: math.PR