{"paper":{"title":"Gaussian and non-Gaussian processes of zero power variation, and related stochastic calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Francesco Russo (UMA), Frederi Viens","submitted_at":"2014-07-17T06:09:49Z","abstract_excerpt":"We consider a class of stochastic processes $X$ defined by $X\\left( t\\right) =\\int_{0}^{T}G\\left( t,s\\right) dM\\left( s\\right) $ for $t\\in\\lbrack0,T]$, where $M$ is a square-integrable continuous martingale and $G$ is a deterministic kernel. Let $m$ be an odd integer. Under the assumption that the quadratic variation $\\left[ M\\right] $ of $M$ is differentiable with $\\mathbf{E}\\left[ \\left\\vert d\\left[ M\\right] (t)/dt\\right\\vert ^{m}\\right] $ finite, it is shown that the $m$th power variation $$ \\lim_{\\varepsilon\\rightarrow0}\\varepsilon^{-1}\\int_{0}^{T}ds\\left( X\\left( s+\\varepsilon\\right) -X\\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4568","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"}