{"paper":{"title":"A discrete approach to Rough Parabolic Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Aur\\'elien Deya (IECN)","submitted_at":"2010-10-30T16:19:01Z","abstract_excerpt":"By combining the formalism of \\cite{RHE} with a discrete approach close to the considerations of \\cite{Davie}, we interpret and solve the rough partial differential equation $dy_t=A y_t \\, dt+\\sum_{i=1}^m f_i(y_t) \\, dx^i_t$ ($t\\in [0,T]$) on a compact domain $\\mathcal{O}$ of $\\R^n$, where $A$ is a rather general elliptic operator of $L^p(\\mathcal{O})$ ($p>1$), $f_i(\\vp)(\\xi):=f_i(\\vp(\\xi))$ and $x$ is the generator of a $2$-rough path. The (global) existence, uniqueness and continuity of a solution is established under classical regularity assumptions for $f_i$. Some identification procedures"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0088","kind":"arxiv","version":3},"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"}