{"paper":{"title":"Fractional smoothness of functionals of diffusion processes under a change of measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.PR","authors_text":"Emmanuel Gobet, Stefan Geiss","submitted_at":"2012-10-16T20:44:33Z","abstract_excerpt":"Let $v:[0,T]\\times \\R^d \\to \\R$ be the solution of the parabolic backward equation $ \\partial_t v + (1/2) \\sum_{i,l} [\\sigma \\sigma^\\perp]_{il} \\partial_{x_i \\partial_{x_l} v + \\sum_{i} b_i \\partial_{x_i}v + kv =0$ with terminal condition $g$, where the coefficients are time- and state-dependent, and satisfy certain regularity assumptions. Let $X=(X_t)_{t\\in [0,T]}$ be the associated $\\R^d$-valued diffusion process on some appropriate $(\\Omega,\\cF,\\Q)$. For $p\\in [2,\\infty)$ and a measure $d\\P=\\lambda_T d\\Q$, where $\\lambda_T$ satisfies the Muckenhoupt condition $A_\\alpha$ for $\\alpha \\in (1,p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4572","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"}