Invariance principles for adaptive self-normalized partial sums processes. (Q1765994)

The paper studies Hölder weak convergence of an adaptive self-normalized partial sums process to a Brownian motion. The authors prove several interesting theorems showing that adaptive self-normalized processes behave pleasantly than the classical partial sums processes. For instance, provided a symmetric law, Hölder weak convergence of an adaptive self-normalized partial sums process to a Brownian motion is equivalent to the property that the law belongs to the normal law domain of attraction. A similar result for the classical partial sums process requires some moment conditions.