Some convergence theorem for random variables in a Hilbert space with application
In this paper, the notion of asymptotically negative dependence for random vectors with values in \({\mathbb R}^d, d\geq1\), is introduced and this notion is generalized to a Hilbert space. Moreover, conditions for almost sure convergence of negatively associated random vectors in a separable real Hilbert space \(H\) are obtained and this result is applied to a linear process generated by \(H\)-valued asymptotically negatively dependent random vectors.
scientific article; zbMATH DE number 6362214