{"paper":{"title":"$\\alpha$-Time Fractional Brownian Motion: PDE Connections and Local Times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Dongsheng Wu, Erkan Nane, Yimin Xiao","submitted_at":"2009-11-02T17:10:24Z","abstract_excerpt":"For $0<\\alpha \\leq 2$ and $0<H<1$, an $\\alpha$-time fractional Brownian motion is an iterated process $Z = \\{Z(t)=W(Y(t)), t \\ge 0\\}$ obtained by taking a fractional Brownian motion $\\{W(t), t\\in \\RR{R} \\}$ with Hurst index $0<H<1$ and replacing the time parameter with a strictly $\\alpha$-stable L\\'evy process $\\{Y(t), t\\geq 0 \\}$ in $\\RR{R}$ independent of $\\{W(t), t \\in \\R\\}$. It is shown that such processes have natural connections to partial differential equations and, when $Y$ is a stable subordinator, can arise as scaling limit of randomly indexed random walks. The existence, joint conti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0357","kind":"arxiv","version":3},"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"}