{"paper":{"title":"Stochastic heat equations driven by L\\'evy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Minsuk Yang, Tongkeun Chang","submitted_at":"2012-05-22T06:13:18Z","abstract_excerpt":"We study stochastic heat equations driven by a class of L\\'evy processes:\ndu = \\De u dt + g dX_t \\quad in \\quad \\bR^d_T, \\qquad u(0,x)= 0 \\quad in \\quad x \\in \\bR^d.\nWe prove the corresponding estimate \\[\\norm{u}_{\\bH_p^k(\\RT)} \\le c(p,T) \\norm{g}_{\\bB_p^{k-\\frac2p}(\\RT)}\\] for $2\\le p<\\infty$ and $k \\in \\bR$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4812","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"}