{"paper":{"title":"On the $\\Phi$-variation of stochastic processes with exponential moments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andreas Basse-O'Connor, Michel Weber","submitted_at":"2015-07-02T14:40:22Z","abstract_excerpt":"We obtain sharp sufficient conditions for exponentially integrable stochastic processes $X=\\{X(t)\\!\\!: t\\in [0,1]\\}$, to have sample paths with bounded $\\Phi$-variation. When $X$ is moreover Gaussian, we also provide a bound of the expectation of the associated $\\Phi$-variation norm of $X$. For an Hermite process $X$ of order $m\\in \\N$ and of Hurst index $H\\in (1/2,1)$, we show that $X$ is of bounded $\\Phi$-variation where $\\Phi(x)=x^{1/H}(\\log(\\log 1/x))^{-m/(2H)}$, and that this $\\Phi$ is optimal. This shows that in terms of $\\Phi$-variation, the Rosenblatt process (corresponding to $m=2$) h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00605","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"}