{"paper":{"title":"Upper Rate Functions of Brownian Motion Type for Symmetric Jump Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jian Wang, Yuichi Shiozawa","submitted_at":"2017-07-13T00:46:38Z","abstract_excerpt":"Let $X$ be a symmetric jump process on $\\R^d$ such that the corresponding jumping kernel $J(x,y)$ satisfies $$J(x,y)\\le \\frac{c}{|x-y|^{d+2}\\log^{1+\\varepsilon}(e+|x-y|)}$$ for all $x,y\\in\\R^d$ with $|x-y|\\ge1$ and some constants $c,\\varepsilon>0$. Under additional mild assumptions on $J(x,y)$ for $|x-y|<1$, we show that $C\\sqrt{r\\log \\log r}$ with some constant $C>0$ is an upper rate function of the process $X$, which enjoys the same form as that for Brownian motions. The approach is based on heat kernel estimates of large time for the process $X$. As a by-product, we also obtain two-sided he"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03942","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"}