Poissonization Inequalities for Sums of Independent Random Variables in Banach Spaces with Applications to Empirical Processes

Abstract

Inequalities are obtained which connect the probability tails and moments of functions of the nth partial sums of independent random variables taking values in a separable Banach space and those for the accompanying infinitely divisible laws. Some applications to empirical processes are studied.

Keywords

• sums of independent random variables
• moment inequalities
• accompanying infinitely divisible law
• convex function
• empirical process