{"paper":{"title":"Some remarks on integral parameters of Wiener process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"A. A. Vladimirov","submitted_at":"2012-12-05T20:39:21Z","abstract_excerpt":"We consider integrals $\\tau_{\\rho}=\\int_0^1\\rho\\xi^2\\,dx$, where $\\xi$ is Wiener process and $\\rho$ is generalized function from some class of multipliers. In the case when multiplier $\\rho$ belongs to the trace-class, it is shown that $\\tau_{\\rho}$ has $\\chi^2$-distribution (or analogous). An example of multiplier $\\rho$ not belonging to the trace-class is constructed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1152","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"}