{"paper":{"title":"On the $\\frac{1}{H}$-variation of the divergence integral with respect to fractional Brownian motion with Hurst parameter $H < 1/2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Nualart, El Hassan Essaky","submitted_at":"2015-01-28T04:46:55Z","abstract_excerpt":"In this paper, we study the $\\frac{1}{H}$-variation of stochastic divergence integrals $X_t = \\int_0^t u_s {\\delta}B_s$ with respect to a fractional Brownian motion $B$ with Hurst parameter $H < \\frac{1}{2}$. Under suitable assumptions on the process u, we prove that the $\\frac{1}{H}$-variation of $X$ exists in $L^1({\\Omega})$ and is equal to $e_H \\int_0^T|u_s|^H ds$, where $e_H = \\mathbb{E}|B_1|^H$. In the second part of the paper, we establish an integral representation for the fractional Bessel Process $\\|B_t\\|$, where $B_t$ is a $d$-dimensional fractional Brownian motion with Hurst paramet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06986","kind":"arxiv","version":1},"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"}