On a multivariate version of Bernstein's inequality
| dc.creator | Major, P. | |
| dc.date | 2004-11-12 | |
| dc.date.accessioned | 2026-07-07T05:14:16Z | |
| dc.date.available | 2026-07-07T05:14:16Z | |
| dc.description | We prove a multivariate version of Bernstein's inequality about the probability that degenerate $U$-statistics take a value larger than some number $u$. This is an improvement of former estimates for the same problem which yields an asymptotically sharp estimate for not too large numbers $u$. This paper also contains an analogous bound about the distribution of multiple Wiener-Ito integrals. Their comparison shows that our results are sharp. The proofs are based on good estimates about high moments of multiple random integrals. They are obtained by means of a diagram formula which enables us to express the product of multiple random integrals as the sum of such expressions. | |
| dc.identifier | https://arxiv.org/abs/math/0411287 | |
| dc.identifier | http://arxiv.org/abs/math/0411287 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73212 | |
| dc.subject | Probability | |
| dc.subject | 60E15 | |
| dc.title | On a multivariate version of Bernstein's inequality | |
| dc.type | text |