{"paper":{"title":"On a new Sheffer class of polynomials related to normal product distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dario Gasbarra, Ehsan Azmoodeh","submitted_at":"2018-02-19T15:35:47Z","abstract_excerpt":"Consider a generic random element $F_\\infty= \\sum_{\\text{finite}} \\lambda_k (N^2_k -1)$ in the second Wiener chaos with a finite number of non-zero coefficients in the spectral representation where $(N_k)_{k \\ge 1}$ is a sequence of i.i.d $\\mathscr{N}(0,1)$. Using the recently discovered (see Arras et al. \\cite{a-a-p-s-stein}) stein operator $\\RR_\\infty$ associated to $F_\\infty$, we introduce a new class of polynomials $$\\PP_\\infty:= \\{ P_n = \\RR^n_\\infty \\textbf{1} \\, : \\, n \\ge 1 \\}.$$ We analysis in details the case where $F_\\infty$ is distributed as the normal product distribution $N_1 \\ti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06671","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"}