| Issue |
ESAIM: PS
Volume 28, 2024
|
|
|---|---|---|
| Page(s) | 329 - 349 | |
| DOI | https://doi.org/10.1051/ps/2024009 | |
| Published online | 15 November 2024 | |
Asymptotic results for compound sums in separable Banach spaces
Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, I-00133 Rome, Italy
* Corresponding author: macci@mat.uniroma2.it
Received:
4
October
2023
Accepted:
7
May
2024
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.
Mathematics Subject Classification: 60F10 / 60G50 / 60B12
Key words: Exponential tightness / large deviations / moderate deviations
© The authors. Published by EDP Sciences, SMAI 2024
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