{"paper":{"title":"BMO estimates for stochastic singular integral operators and its application to PDEs with L\\'{e}vy noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guangying Lv, Hongjun Gao, Jiang-Lun Wu, Jinlong Wei","submitted_at":"2017-04-19T01:57:44Z","abstract_excerpt":"In this paper, we consider the stochastic singular integral operators and obtain the BMO estimates. As an application, we consider the fractional Laplacian equation with additive noises\n  \\bess du_t(x)=\\Delta^{\\frac{\\alpha}{2}}u_t(x)dt+\\sum_{k=1}^\\infty\\int_{\\mathbb{R}^m}g^k(t,x)z\\tilde N_k(dz,dt),\\ \\ \\ u_0=0,\\ 0\\leq t\\leq T,\n  \\eess where $\\Delta^{\\frac{\\alpha}{2}}=-(-\\Delta)^{\\frac{\\alpha}{2}}$, and $\\int_{\\mathbb{R}^m}z\\tilde N_k(t,dz)=:Y_t^k$ are independent $m$-dimensional pure jump L\\'{e}vy processes with L\\'{e}vy measure of $\\nu^k$. Following the idea of \\cite{Kim}, we obtain the $q$-th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05577","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"}