{"paper":{"title":"Image sets of fractional Brownian sheets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Paul Balan\\c{c}a","submitted_at":"2015-07-30T11:55:09Z","abstract_excerpt":"Let $B^H = \\{ B^H(t), t\\in\\mathbb{R}^N \\}$ be an $(N,d)$-fractional Brownian sheet with Hurst index $H=(H_1,\\dotsc,H_N)\\in (0,1)^N$. The main objective of the present paper is to study the Hausdorff dimension of the image sets $B^H(F+t)$, $F\\subset\\mathbb{R}^N$ and $t\\in\\mathbb{R}^N$, in the dimension case $d<\\tfrac{1}{H_1}+\\cdots+\\tfrac{1}{H_N}$. Following the seminal work of Kaufman (1989), we establish uniform dimensional properties on $B^H$, answering questions raised by Khoshnevisan et al (2006) and Wu and Xiao (2009).\n  For the purpose of this work, we introduce a refinement of the secto"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08466","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"}