A functional limit theorem for self-normalized partial sum processes in the $M_{1}$ topology
Probability
2026-05-12 v2
Abstract
For a stationary sequence of random variables we derive a self-normalized functional limit theorem under joint regular variation with index and weak dependence conditions. The convergence takes place in the space of real-valued cadlag functions on with the Skorokhod topology.
Cite
@article{arxiv.2411.18236,
title = {A functional limit theorem for self-normalized partial sum processes in the $M_{1}$ topology},
author = {Danijel Krizmanic},
journal= {arXiv preprint arXiv:2411.18236},
year = {2026}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1704.02121