{"paper":{"title":"On multifractality and fractional derivatives","license":"","headline":"","cross_cats":["cond-mat.stat-mech","math.PR","q-fin.ST"],"primary_cat":"nlin.CD","authors_text":"T. Matsumoto, U. Frisch","submitted_at":"2001-07-25T04:11:15Z","abstract_excerpt":"It is shown phenomenologically that the fractional derivative $\\xi=D^\\alpha u$ of order $\\alpha$ of a multifractal function has a power-law tail $\\propto |\\xi| ^{-p_\\star}$ in its cumulative probability, for a suitable range of $\\alpha$'s. The exponent is determined by the condition $\\zeta_{p_\\star} = \\alpha p_\\star$, where $\\zeta_p$ is the exponent of the structure function of order $p$. A detailed study is made for the case of random multiplicative processes (Benzi {\\it et al.} 1993 Physica D {\\bf 65}: 352) which are amenable to both theory and numerical simulations. Large deviations theory "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0107057","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"}