{"paper":{"title":"Ito formula for mild solutions of SPDEs with Gaussian and non-Gaussian noise and applications to stability properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"B. R\\\"udiger, B. Sarkar, L. Gawarecki, S. Albeverio, V. Mandrekar","submitted_at":"2016-12-30T10:07:35Z","abstract_excerpt":"We use Yosida approximation to find an It\\^o formula for mild solutions $\\left\\{X^x(t), t\\geq 0\\right\\}$ of SPDEs with Gaussian and non-Gaussian coloured noise, the non Gaussian noise being defined through compensated Poisson random measure associated to a L\\'evy process. The functions to which we apply such It\\^o formula are in $C^{1,2}([0,T]\\times H)$, as in the case considered for SDEs in [9]. Using this It\\^o formula we prove exponential stability and exponential ultimate boundedness properties in mean square sense for mild solutions. We also compare such It\\^o formula to an It\\^o formula "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09440","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"}