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Moments for self-normalized partial sums — arXiv:2609.03728

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.03728
License (as archived): CC0-1.0
Archived: 2026-10-17T02:32:02.360Z
SHA-256 of the archived text: d811ab5a53fd3707f6e87f183fdd1870769b27ba95227d883856bd466c4beaf7
Stable URL of this page: https://metraipolis.com/documento/dc_00a4233b6239

How to cite

Moments for self-normalized partial sums — arXiv:2609.03728 — arXiv (en), https://arxiv.org/abs/2609.03728 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_00a4233b6239 (Metraipolis archive dc_00a4233b6239, sha256 d811ab5a53fd3707f6e87f183fdd1870769b27ba95227d883856bd466c4beaf7)

BibTeX

@misc{dc00a4233b6239,
  title = {Moments for self-normalized partial sums — arXiv:2609.03728},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.03728},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_00a4233b6239; sha256 d811ab5a53fd3707f6e87f183fdd1870769b27ba95227d883856bd466c4beaf7},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.03728. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-04 in math.PR).
Categorie arXiv: Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.03728 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T02:08:47.864Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-04?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).