Asymptotic expansions for the Laplace approximations of sums of Banach space-valued random variables
| dc.creator | Albeverio, Sergio | |
| dc.creator | Liang, Song | |
| dc.date | 2005-03-25 | |
| dc.date.accessioned | 2026-07-07T05:18:30Z | |
| dc.date.available | 2026-07-07T05:18:30Z | |
| dc.description | Let X_i, i\in N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let Φbe a smooth enough mapping from B into R. An asymptotic evaluation of Z_n=E(\exp (nΦ(\sum_{i=1}^nX_i/n))), up to a factor (1+o(1)), has been gotten in Bolthausen [Probab. Theory Related Fields 72 (1986) 305-318] and Kusuoka and Liang [Probab. Theory Related Fields 116 (2000) 221-238]. In this paper, a detailed asymptotic expansion of Z_n as n\to \infty is given, valid to all orders, and with control on remainders. The results are new even in finite dimensions. | |
| dc.description | Published at http://dx.doi.org/10.1214/009117904000001017 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0503601 | |
| dc.identifier | http://arxiv.org/abs/math/0503601 | |
| dc.identifier | Annals of Probability 2005, Vol. 33, No. 1, 300-336 | |
| dc.identifier | doi:10.1214/009117904000001017 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74680 | |
| dc.subject | Probability | |
| dc.subject | 62E20, 60F10, 60B12. (Primary) | |
| dc.title | Asymptotic expansions for the Laplace approximations of sums of Banach space-valued random variables | |
| dc.type | text |