{"paper":{"title":"Brownian semistationary processes and related processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Orimar Sauri","submitted_at":"2017-10-16T13:56:37Z","abstract_excerpt":"In this paper we find a pathwise decomposition of a certain class of Brownian semistationary processes ($\\mathcal{BSS}$) in terms of fractional Brownian motions. To do this, we specialize in the case when the kernel of the $\\mathcal{BSS}$ is given by $\\varphi_{\\alpha}\\left(x\\right)=L\\left(x\\right)x^{\\alpha}$ with $\\alpha\\in(-1/2,0)\\cup(0,1/2)$ and $L$ a continuous function slowly varying at zero. We use this decomposition to study some path properties and derive It\\^o's formula for this subclass of $\\mathcal{BSS}$ processes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05694","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"}