{"paper":{"title":"On (signed) Takagi-Landsberg functions: $p^{\\text{th}}$ variation, maximum, and modulus of continuity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Schied, Yuliya Mishura","submitted_at":"2018-06-14T18:48:59Z","abstract_excerpt":"We study a class $\\mathfrak X^H$ of signed Takagi-Landsberg functions with Hurst parameter $H\\in(0,1)$. We first show that the functions in $\\mathfrak X^H$ admit a linear $p^{\\text{th}}$ variation along the sequence of dyadic partitions of $[0,1]$, where $p=1/H$. The slope of the linear increase can be represented as the $p^{\\text{th}}$ absolute moment of the infinite Bernoulli convolution with parameter $2^{H-1}$. The existence of a continuous $p^{\\text{th}}$ variation enables the use of the functions in $\\mathfrak X^H$ as test integrators for higher-order pathwise It\\^o calculus. Our next re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05702","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}