{"paper":{"title":"Optimal local H\\\"{o}lder index for density states of superprocesses with $(1+\\beta)$-branching mechanism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Klaus Fleischmann, Leonid Mytnik, Vitali Wachtel","submitted_at":"2008-05-26T10:44:07Z","abstract_excerpt":"For $0<\\alpha\\leq2$, a super-$\\alpha$-stable motion $X$ in $\\mathsf{R}^d$ with branching of index $1+\\beta\\in(1,2)$ is considered. Fix arbitrary $t>0$. If $d<\\alpha/\\beta$, a dichotomy for the density function of the measure $X_t$ holds: the density function is locally H\\\"{o}lder continuous if $d=1$ and $\\alpha>1+\\beta$ but locally unbounded otherwise. Moreover, in the case of continuity, we determine the optimal local H\\\"{o}lder index."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.3914","kind":"arxiv","version":4},"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"}