{"paper":{"title":"A representation for the derivative with respect to the initial data of the solution of an SDE with a non-regular drift and a Gaussian noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrey Pilipenko, Olga Aryasova","submitted_at":"2016-05-23T07:11:18Z","abstract_excerpt":"We consider a multidimensional SDE with a Gaussian noise and a drift vector being a vector function of bounded variation. We prove the existence of generalized derivative of the solution with respect to the initial conditions and represent the derivative as a solution of a linear SDE with coefficients depending on the initial process. The representation obtained is a natural generalization of the expression for the derivative in the smooth case. The theory of continuous additive functionals is used."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06911","kind":"arxiv","version":2},"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"}