A maximal inequality for exchangeable systems of random variables (Q2726276)

The aim of this paper is to investigate the distribution of \(a_{n}:=\max_{k\leq n}\|\xi_{1}+\dots +\xi_{k}\|\) for an exchangeable system of random variables \((\xi_{1},\dots ,\xi_{n})\), \(\sum_{1}^{n}\xi_{j}=0\), taking values in a normed space \(X\). By an exchangeable system of random variables (or simply exchangeable random variables) \((\xi_{1},\dots ,\xi_{n})\) it is understood a system whose joint distribution does not change under any of its rearrangement. It is proved that the tail probability of \(a_{n}\) is equivalent to that of \(\sum_{1}^{n}\xi_{j}r_{j},\) where \((r_{1},\dots ,r_{n})\) is a Rademacher system independent of \((\xi_{1},\dots ,\xi_{n})\).NEWLINENEWLINEFor the entire collection see [Zbl 0956.00022].