{"paper":{"title":"H\\\"{o}lder continuity of the solutions to a class of SPDEs arising from multidimensional superprocesses in random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Nualart, Panqiu Xia, Yaozhong Hu","submitted_at":"2018-10-18T15:46:11Z","abstract_excerpt":"We consider a $d$-dimensional branching particle system in a random environment. Suppose that the initial measures converge weakly to a measure with bounded density. Under the Mytnik-Sturm branching mechanism, we prove that the corresponding empirical measure $X_t^n$ converges weakly in the Skorohod space $D([0,T];M_F(\\mathbb{R}^d))$ and the limit has a density $u_t(x)$, where $M_F(\\mathbb{R}^d)$ is the space of finite measures on $\\mathbb{R}^d$. We also derive a stochastic partial differential equation $u_t(x)$ satisfies. By using the techniques of Malliavin calculus, we prove that $u_t(x)$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08120","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"}