{"paper":{"title":"Lower Bounds of the Hausdorff dimension for Feller processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jian Wang, Ren\\'e L. Schilling, Victoria Knopova","submitted_at":"2014-06-15T19:12:11Z","abstract_excerpt":"Let $(X_t)_{t\\ge0}$ be a Feller process generated by a pseudo-differential operator whose symbol satisfies $\\|p(\\cdot,\\xi)\\|_\\infty\\le c(1+|\\xi|^2)$ and $p(\\cdot,0)\\equiv0.$ We prove that, for a large class of examples, the Hausdorff dimension of the set $\\{X_t: t\\in E\\}$ for any analytic set $E\\subset [0,\\infty)$ is almost surely bounded below by $\\betalower \\Dh E$, where \\begin{align*}\n  \\betalower&:=\\sup\\left\\{\\delta>0: \\lim_{|\\xi|\\to \\infty} \\frac{\\inf_{z\\in\\R^d} \\Re p(z,\\xi)}{|\\xi|^\\delta}=\\infty\\right\\}. \\end{align*}This, along with the upper bound $ \\betaupperstar \\Dh E$ with \\begin{ali"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3849","kind":"arxiv","version":2},"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"}