{"paper":{"title":"Translation Invariant Diffusions in the space of tempered distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"B. Rajeev","submitted_at":"2017-06-28T09:33:16Z","abstract_excerpt":"In this paper we prove existence and pathwise uniqueness for a class of stochastic differential equations (with coefficients $\\sigma_{ij},b_i$ and initial condition $y$ in the space of tempered distributions) that maybe viewed as a generalisation of Ito's original equations with smooth coefficients . The solutions are characterized as the translates of a finite dimensional diffusion whose coefficients $\\sigma_{ij}\\star \\tilde{y},b_i\\star \\tilde{y}$ are assumed to be locally Lipshitz.Here $\\star$ denotes convolution and $\\tilde{y}$ is the distribution which on functions, is realised by the form"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09184","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"}