{"paper":{"title":"Weak Solutions of stochastic recursions: an explicit construction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pascal Moyal","submitted_at":"2009-04-21T12:51:28Z","abstract_excerpt":"We propose an explicit construction of the solution of a stationary stochastic recursion of the form $X\\circ\\theta=\\phi(X)$ on a semi-ordered Polish space, when the monotonicity of $\\phi$ is not assumed. This solution exists on an enriched probability space (it is said \\emph{weak}), provided the recursion is lattice-valued, and dominated by a proper monotonic stochastic recursion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.3240","kind":"arxiv","version":2},"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"}