Asymptotic results for compound sums in separable Banach spaces

Claudio Macci; Barbara Pacchiarotti

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arXiv · 2303.08788

Asymptotic results for compound sums in separable Banach spaces

Claudio Macci·Barbara Pacchiarotti

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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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Claudio Macci, Barbara Pacchiarotti. 2023-03-15. Asymptotic results for compound sums in separable Banach spaces. https://arxiv.org/abs/2303.08788

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