{"paper":{"title":"Random series of functions and applications","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dominique Schneider (LMPA), Fr\\'ed\\'eric Paccaut (LAMFA)","submitted_at":"2006-02-10T09:29:09Z","abstract_excerpt":"We study the continuity properties of trajectories for some random series of functions $\\sum a\\_kf(\\alpha X\\_k(\\omega))$ where $a\\_k$ is a complex sequence, $X\\_k$ a sequence of real independent random variables, $f$ is a real valued function with period one and summable Fourier coefficients. We obtain almost sure continuity results for these periodic or almost periodic series for a large class of functions, where the \"almost sure\" does not depend on the function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0602207","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":""},"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"}