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Asymptotic results for compound sums in separable Banach spaces

Published 15 Mar 2023 in math.PR | (2303.08788v3)

Abstract: We prove large and moderate deviation results for sequences of compound sums, where the summands are i.i.d. random variables taking values in a separable 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.

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