Asymptotic results for compound sums in Banach Spaces

Claudio Macci, Barbara Pacchiarotti

Published 2023-03-15Version 1

We prove large and moderate deviation results for sequences of compound sums, where the summands are i.i.d. random variables taking values on a Banach space. We establish that the results hold by proving that we are dealing with exponentially tight sequences. We present two moderate deviation results: in the first one the summands are centered, in the second one the compound sums are centered.