{"paper":{"title":"Analytic Evaluation of the Fractional Moments for the Quasi-Stationary Distribution of the Shiryaev Martingale on an Interval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.OT"],"primary_cat":"stat.CO","authors_text":"Aleksey S. Polunchenko, Andrey Pepelyshev, Kexuan Li","submitted_at":"2019-04-05T09:46:54Z","abstract_excerpt":"We consider the quasi-stationary distribution of the classical Shiryaev diffusion restricted to the interval $[0,A]$ with absorption at a fixed $A>0$. We derive analytically a closed-form formula for the distribution's fractional moment of an {\\em arbitrary} given order $s\\in\\mathbb{R}$; the formula is consistent with that previously found by Polunchenko and Pepelyshev (2018) for the case of $s\\in\\mathbb{N}$. We also show by virtue of the formula that, if $s<1$, then the $s$-th fractional moment of the quasi-stationary distribution becomes that of the exponential distribution (with mean $1/2$)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02961","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"}