{"paper":{"title":"Invariant sample measures and sample statistical solutions for nonautonomous stochastic lattice Cahn-Hilliard equation with nonlinear noise","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Chunqiu Li, Dongdong Zhu, Jintao Wang","submitted_at":"2024-04-23T07:23:28Z","abstract_excerpt":"We consider a stochastic lattice Cahn-Hilliard equation with nonautonomous nonlinear noise. First, we prove the existence of pullback random attractors in $\\ell^2$ for the generated nonautonomous random dynamical system. Then, we construct the time-dependent invariant sample Borel probability measures based on the pullback random attractor. Moreover, we develop a general stochastic Liouville type equation for nonautonomous random dynamical systems and show that the invariant sample measures obtained satisfy the stochastic Liouville type equation. At last, we define a new kind of statistical so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.14798","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.14798/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}