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Limit theory for a class of non-stationary linear processes with weakly dependent heavy-tailed innovations
Abstract
For a class of non-stationary linear processes (Xn)n with weakly dependent heavy-tailed innovations we prove a convergence result for the space-time point processes Nn=∑i=1nδ(i/n, Xi/an). Using this result and the continuous mapping theorem we then derive functional convergence of the corresponding partial maxima process in the space of càdlàg functions on [0,1].
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BibTeX
@misc{krizmanic2026limit,
title = {{Limit theory for a class of non-stationary linear processes with weakly dependent heavy-tailed innovations}},
author = {Danijel Krizmanic},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32636},
eprint = {2609.32636},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32636},
}
RIS
TY - UNPB
TI - Limit theory for a class of non-stationary linear processes with weakly dependent heavy-tailed innovations
AU - Danijel Krizmanic
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32636
UR - https://arxiv.org/abs/2609.32636
AB - For a class of non-stationary linear processes (X_n)_n with weakly dependent heavy-tailed innovations we prove a convergence result for the space-time point processes N_n=∑_i=1^nδ_(i/n, X_i/a_n). Using this result and the continuous mapping theorem we then derive functional convergence of the corresponding partial maxima process in the space of càdlàg functions on [0,1].
ER -