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Quadratic and $p$-th variation of random signed Takagi--Landsberg bridges — arXiv:2609.21688

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.21688
License (as archived): CC0-1.0
Archived: 2026-10-10T02:07:21.719Z
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How to cite

Quadratic and $p$-th variation of random signed Takagi--Landsberg bridges — arXiv:2609.21688 — arXiv (en), https://arxiv.org/abs/2609.21688 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_d64f0269eabe (Metraipolis archive dc_d64f0269eabe, sha256 4ccc22f62d0404746334c000641bb6341b6797911b9cc1c657ec467cd2b3c3c2)

BibTeX

@misc{dcd64f0269eabe,
  title = {Quadratic and $p$-th variation of random signed Takagi--Landsberg bridges — arXiv:2609.21688},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.21688},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_d64f0269eabe; sha256 4ccc22f62d0404746334c000641bb6341b6797911b9cc1c657ec467cd2b3c3c2},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.21688. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study random signed Takagi--Landsberg bridges with independent Rademacher Faber--Schauder coefficients. At index $H=1/2$, we prove that every fixed deterministic refining sequence of partitions with vanishing mesh yields quadratic variation $t$, almost surely and uniformly in $t\in[0,1]$. For partitions that need not be refining, the mesh condition $o(1/\log n)$ is sufficient, and its order is sharp. Our proofs use an operator representation of the quadratic sums and moment bounds for Rademacher chaos. We also show that asymmetric signs can destroy this invariance. At every index $H\ne1/2$, we construct a deterministic refining sequence along which the critical $p$-power sums, with $p=1/H$, have two distinct finite accumulation points almost surely. At $H=1/4$, uniform thirds grids provide an explicit alternative to the dyadic limit. Thus $H=1/2$ is the unique index in the symmetric family at which critical variation is invariant along every fixed deterministic refining sequence. Nevertheless the variation index equals $1/H$ almost surely across a large sequence of partitions.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-21 in math.PR).
Categorie arXiv: Probability (math.PR) ; Mathematical Finance (q-fin.MF).
Pagina del lavoro: https://arxiv.org/abs/2609.21688 — 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 2026-10-10T01:47:50.205Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-21?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).