{"paper":{"title":"An Ornstein-Uhlenbeck process associated to self-normalized sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Amites Dasgupta, Gopal K. Basak","submitted_at":"2013-02-01T12:12:33Z","abstract_excerpt":"We consider an Ornstein-Uhleneck (OU) process associated to self-normalised sums in i.i.d. symmetric random variables from the domain of attraction of $N(0, 1)$ distribution. We proved the self-normalised sums converge to the OU process (in $C[0, \\infty)$). Importance of this is that the OU process is a stationary process as opposed to the Brownian motion, which is a non-stationary distribution (see for example, the invariance principle proved by Csorgo et al (2003, Ann Probab) for self-normalised sums that converges to Brownian motion). The proof uses recursive equations similar to those that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0158","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"}