{"paper":{"title":"Thin tails of fixed points of the nonhomogeneous smoothing transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gerold Alsmeyer, Piotr Dyszewski","submitted_at":"2015-10-21T22:48:13Z","abstract_excerpt":"For a given random sequence $(C,T_{1},T_{2},\\ldots)$ with nonzero $C$ and a.s. finite number of nonzero $T_{k}$, the nonhomogeneous smoothing transform $\\mathcal{S}$ maps the law of a real random variable $X$ to the law of $\\sum_{k\\ge 1}T_{k}X_{k}+C$, where $X_{1},X_{2},\\ldots$ are independent copies of $X$ and also independent of $(C,T_{1},T_{2},\\ldots)$. This law is a fixed point of $\\mathcal{S}$ if the stochastic fixed-point equation (SFPE) $X\\stackrel{d}{=}\\sum_{k\\ge 1}T_{k}X_{k}+C$ holds true, where $\\stackrel{d}{=}$ denotes equality in law. Under suitable conditions including $\\mathbb{E}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06451","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"}