{"paper":{"title":"An extension of the L\\'{e}vy characterization to fractional Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Esko Valkeila, Yuliya Mishura","submitted_at":"2006-11-29T11:45:20Z","abstract_excerpt":"Assume that $X$ is a continuous square integrable process with zero mean, defined on some probability space $(\\Omega,\\mathrm {F},\\mathrm {P})$. The classical characterization due to P. L\\'{e}vy says that $X$ is a Brownian motion if and only if $X$ and $X_t^2-t$, $t\\ge0,$ are martingales with respect to the intrinsic filtration $\\mathrm {F}^X$. We extend this result to fractional Brownian motion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611913","kind":"arxiv","version":4},"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"}