Maximal inequalities for partial sums of independent random vectors with multi dimensional time parameters

Abstract

We obtain upper and lower bounds on the distribution of the partial sums constructed from a multi-dimensional array of independent random vectors. These bounds include, among others, generalizations of some of the well known classical inequalities such as the converse Kolmogorov and the Skorokhod-Ottaviani maximal inequalities.

Keywords:

• Multi-dimensional array of random vectors
• Maximal inequalities