An estimate on the maximum of a nice class of stochastic integrals
| dc.creator | Major, Peter | |
| dc.date | 2003-10-20 | |
| dc.date.accessioned | 2026-07-07T05:02:07Z | |
| dc.date.available | 2026-07-07T05:02:07Z | |
| dc.description | Let a sequence of iid. random variables $ξ_1,...,ξ_n$ be given on a space $(X,\cal X)$ with distribution $μ$ together with a nice class $\cal F$ of functions $f(x_1,...,x_k)$ of $k$ variables on the product space $(X^k,{\cal X}^k)$. For all $f\in\cal F$ we consider the random integral $J_{n,k}(f)$ of the function $f$ with respect to the $k$-fold product of the normalized signed measure $\sqrt n(μ_n-μ)$, where $μ_n$ denotes the empirical measure defined by the random variables $ξ_1,...,ξ_n$ and investigate the probabilities $P(\sup_{f\in {\cal F}}|J_{n,k}(f)|>x)$ for all $x>0$. We show that for nice classes of functions, for instance if $\cal F$ is a Vapnik-Cervonenkis class, an almost as good bound can be given for these probabilities as in the case when only the random integral of one function is considered. | |
| dc.description | This article can also be found at my homepage http://www.renyi.hu/~major/public1.html | |
| dc.identifier | https://arxiv.org/abs/math/0310324 | |
| dc.identifier | http://arxiv.org/abs/math/0310324 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68932 | |
| dc.subject | Probability | |
| dc.title | An estimate on the maximum of a nice class of stochastic integrals | |
| dc.type | text |