A functional limit theorem for self-normalized partial sum processes in the $M_{1}$ topology

Danijel Krizmanic

paper

A functional limit theorem for self-normalized partial sum processes in the $M_{1}$ topology

arXiv:2411.18236

Abstract

For a stationary sequence of random variables we derive a self-normalized functional limit theorem under joint regular variation with index $I^\pm \in (0, 2)$ and weak dependence conditions. The convergence takes place in the space of real-valued cadlag functions on $[0, 1]$ with the Skorokhod $M_{1}$ topology.

arXiv admin note: substantial text overlap with arXiv:1704.02121

A functional limit theorem for self-normalized partial sum processes in the M1​ topology

Abstract

A functional limit theorem for self-normalized partial sum processes in the $M_{1}$ topology