{"paper":{"title":"Wave equation with a coloured stable noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Georgiy Shevchenko, Larysa Pryhara","submitted_at":"2017-07-26T12:57:54Z","abstract_excerpt":"We define a random measure generated by a real anisotropic harmonizable fractional stable field $Z^H$ with stability parameter $\\alpha\\in(1,2)$ and Hurst index $H\\in(1/2,1)$ and prove that the measure is $\\sigma$-additive in probability. An integral with respect to this measure is constructed, which enables us to consider a wave equation in $\\mathbb R^3$ with a random source generated by $Z^H$. We show that the solution to this equation, given by Kirchhoff's formula, has a modification, which is H\\\"older continuous of any order up to $(3H-1)\\wedge 1$. In the case where $H\\in(2/3,1)$, we show f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08415","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"}