{"paper":{"title":"Process convergence of self normalized sums of i.i.d. random variables coming from domain of attraction of stable distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arunangshu Biswas, G K Basak","submitted_at":"2010-08-02T10:53:52Z","abstract_excerpt":"In this paper we show that the continuous version of the self normalised process $Y_{n,p}(t)= S_n(t)/V_{n,p}+(nt-[nt])X_{[nt]+1}/V_{n,p}$ where $S_n(t)=\\sum_{i=1}^{[nt]} X_i$ and $V_{(n,p)}= \\sum_{i=1}^{n}|X_i|^p)^{\\frac{1}{p}}$ and $X_i$ i.i.d. random variables belong to $DA(\\alpha)$, has a non trivial distribution iff $p=\\alpha=2$. The case\nfor $2 > p > \\alpha$ and $p \\le \\alpha < 2$\nis systematically eliminated by showing that either of tightness or finite\ndimensional convergence to a non-degenerate limiting distribution does not hold. This work is an extension of the work by Cs\\\"org\\\"o et "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0276","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"}