{"paper":{"title":"General alpha-Wiener bridges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Matyas Barczy, Peter Kern","submitted_at":"2011-02-21T17:47:21Z","abstract_excerpt":"An alpha-Wiener bridge is a one-parameter generalization of the usual Wiener bridge, where the parameter alpha>0 represents a mean reversion force to zero. We generalize the notion of alpha-Wiener bridges to continuous functions $\\alpha:[0,T)\\to R$. We show that if the limit $\\lim_{t\\uparrow T}\\alpha(t)$ exists and is positive, then a general alpha-Wiener bridge is in fact a bridge in the sense that it converges to 0 at time T with probability one. Further, under the condition $\\lim_{t\\uparrow T}\\alpha(t)\\ne 1$ we show that the law of the general alpha-Wiener bridge can not coincide with the l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4288","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"}