{"paper":{"title":"M\\\"untz linear transforms of Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ching-Tang Wu, Larbi Alili","submitted_at":"2011-12-17T16:27:05Z","abstract_excerpt":"We consider a class of linear Volterra transforms of Brownian motion associated to a sequence of M\\\"untz Gaussian spaces and determine explicitly their kernels; some interesting links with M\\\"untz-Legendre polynomials are provided. This gives new explicit examples of progressive Gaussian enlargement of the Brownian filtration. By exploiting a link to stationarity, we give a necessary and sufficient condition for the existence of kernels of infinite order associated to an infinite dimensional M\\\"untz Gaussian space; we also examine when the transformed Brownian motion remains a semimartingale i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4071","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"}