{"paper":{"title":"Renormalized self-intersection local time for fractional Brownian motion","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Nualart, Yaozhong Hu","submitted_at":"2005-06-29T10:35:28Z","abstract_excerpt":"Let B_t^H be a d-dimensional fractional Brownian motion with Hurst parameter H\\in(0,1). Assume d\\geq2. We prove that the renormalized self-intersection local time\\ell=\\int_0^T\\int_0^t\\delta(B_t^H-B_s^H) ds dt -E\\biggl(\\int_0^T\\int_0^t\\delta (B_t^H-B_s^H) ds dt\\biggr) exists in L^2 if and only if H<3/(2d), which generalizes the Varadhan renormalization theorem to any dimension and with any Hurst parameter. Motivated by a result of Yor, we show that in the case 3/4>H\\geq\\frac{3}{2d}, r(\\epsilon)\\ell_{\\epsilon} converges in distribution to a normal law N(0,T\\sigma^2), as \\epsilon tends to zero, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506592","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0506592/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}