Rosenthal type inequalities for \(B\)-valued strong mixing random fields and their applications
The main result of the paper is a Rosenthal-type inequality for the partial sums of a strongly mixing random field with values in a Banach space \(B\). The notion of mixing is based on a maximal correlation coefficient where the correlations are taken from random variables with values in \(B\) and in its dual space \(B^\star\), respectively. \(B\) must be of Rademacher type \(p\). Furthermore either \(B^\star\) must have the Radon-Nikodym property or \(B\) has to be reflexive. Some applications on the weak law of large numbers for \(B\)-valued mixing sequences and on the Marcinkiewicz-Zygmund laws for \(B\)-valued mixing fields are given.
scientific article; zbMATH DE number 1207232