Peer-reviewedCC BY 4.0Stochastic Processes and their Applications
Moments for self-normalized partial sums
Abstract
We consider a regularly varying stationary sequence of random variables (Xt) with tail index < 2. For these sequences we study the joint convergence of sums, `p- type moduli and maxima. We focus on ratio statistics, including the studentized sums and sums normalized by the corresponding maxima, and study the existence of moments for the limit ratios. We consider particular examples of processes (Xt) whose limit ratios possess all moments. But, in contrast to the latter situation, there also exist sequences (Xt) where certain moments of the limit ratio are in nite. This phenomenon results from extremal clusters in the sequence.
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BibTeX
@article{matsui2026moments,
title = {{Moments for self-normalized partial sums}},
author = {Muneya Matsui and Thomas Mikosch and Olivier Wintenberger},
journal = {Stochastic Processes and their Applications},
year = {2026},
month = sep,
doi = {10.1016/j.spa.2025.104810},
eprint = {2609.03728},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05734735v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Moments for self-normalized partial sums
AU - Muneya Matsui
AU - Thomas Mikosch
AU - Olivier Wintenberger
PY - 2026
DA - 2026/09/01
JO - Stochastic Processes and their Applications
DO - 10.1016/j.spa.2025.104810
UR - https://hal.science/hal-05734735v1
AB - We consider a regularly varying stationary sequence of random variables (Xt) with tail index < 2. For these sequences we study the joint convergence of sums, `p- type moduli and maxima. We focus on ratio statistics, including the studentized sums and sums normalized by the corresponding maxima, and study the existence of moments for the limit ratios. We consider particular examples of processes (Xt) whose limit ratios possess all moments. But, in contrast to the latter situation, there also exist sequences (Xt) where certain moments of the limit ratio are in nite. This phenomenon results from extremal clusters in the sequence.
SN - 0304-4149
SN - 1879-209X
ER -