{"paper":{"title":"Wavelet Series Representation and Geometric Properties of Harmonizable Fractional Stable Sheets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Antoine Ayache, Narn-Rueih Shieh, Yimin Xiao","submitted_at":"2019-03-11T16:09:22Z","abstract_excerpt":"Let $Z^H= \\{Z^H(t), t \\in \\R^N\\}$ be a real-valued $N$-parameter harmonizable fractional stable sheet with index $H = (H_1, \\ldots, H_N) \\in (0, 1)^N$. We establish a random wavelet series expansion for $Z^H$ which is almost surely convergent in all the H\\\"older spaces $C^\\gamma ([-M,M]^N)$, where $M>0$ and $\\gamma\\in (0, \\min\\{H_1,\\ldots, H_N\\})$ are arbitrary. One of the main ingredients for proving the latter result is the LePage representation for a rotationally invariant stable random measure.\n  Also, let $X=\\{X(t), t \\in \\R^N\\}$ be an $\\R^d$-valued harmonizable fractional stable sheet wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04397","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"}