{"paper":{"title":"Some extensions of fractional Brownian motion and sub-fractional Brownian motion related to particle systems","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anna Talarczyk, Luis G. Gorostiza, Tomasz Bojdecki","submitted_at":"2007-02-23T16:44:31Z","abstract_excerpt":"In this paper we study three self-similar, long-range dependence, Gaussian processes. The first one, with covariance\n  \\int_0^{s\\wedge t} u^a [(t-u)^b+(s-u)^b]du, parameters a>-1, -1<b\\leq 1, |b|\\leq 1+a, corresponds to fractional Brownian motion for a=0, -1<b<1. The second one, with covariance (2-h)(s^h+t^h-[(s+t)^h +|s-t|^h]/2), parameter 0<h\\leq 4, corresponds to sub-fractional Brownian motion for 0<h<2. The third one, with covariance -(s^2\\log s + t^2\\log t -[(s+t)^2 \\log (s+t) +(s-t)^2 \\log |s-t|]/2), is related to the second one. These processes come from occupation time fluctuations of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702708","kind":"arxiv","version":2},"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"}