{"paper":{"title":"Path-dependent It\\^o formulas under finite $(p,q)$-variation regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alberto Ohashi, Evelina Shamarova, Nikolai N. Shamarov","submitted_at":"2015-05-05T04:33:17Z","abstract_excerpt":"In this work, we establish pathwise functional It\\^o formulas for non-smooth functionals of real-valued continuous semimartingales. Under finite $(p,q)$-variation regularity assumptions in the sense of two-dimensional Young integration theory, we establish a pathwise local-time decomposition\n  $$F_t(X_t) = F_0(X_0)+ \\int_0^t\\nabla^hF_s(X_s)ds + \\int_0^t\\nabla^wF_s(X_s)dX(s) - \\frac{1}{2}\\int_{-\\infty}^{+\\infty}\\int_0^t(\\nabla^w_xF_s)(^{x}X_s)d_{(s,x)}\\ell^x(s).$$ Here, $X_t= \\{X(s); 0\\le s\\le t\\}$ is the continuous semimartingale path up to time $t\\in [0,T]$, $\\nabla^h$ is the horizontal deriv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00879","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"}