Estimates for the closeness of successive convolutions of multidimensional symmetric distributions
Let \(\xi _ 1,\xi _ 2,...\), be i.i.d. random vectors in \({\mathbb{R}}^ k\) with a common distribution \({\mathcal L}(\xi _ i)=F\), \(i=1,2,...\). Let \(S_ n=\xi _ 1+...+\xi _ n\). We investigate how small is the difference between \({\mathcal L}(S_ n)\) and \({\mathcal L}(S_{n+m})\) in the case when \(\xi _ i\) have symmetric distributions.
scientific article; zbMATH DE number 4026438
scientific article