{"paper":{"title":"Two-time, response-excitation moment equations for a cubic half-oscillator under Gaussian and cubic-Gaussian colored excitation. Part 1: The monostable case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gerassimos A. Athanassoulis, Ivi C. Tsantili, Zacharias G. Kapelonis","submitted_at":"2013-04-08T13:05:17Z","abstract_excerpt":"In this paper a new method is presented for the formulation and solution of two-time, response-excitation moment equations for a nonlinear dynamical system excited by colored, Gaussian or non-Gaussian processes. Starting from equations for the two-time moments (e.g. for Cxy(t,s), Cxx(t,s)), the method uses an exact time-closure condition, in addition to a Gaussian moment closure, in order to obtain a closed, non-local in time (causal) subsystem for the one-time (t=s) moments. After solving this causal system, the two-time moments can be calculated for all (t,s) pairs as well. The present metho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2195","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"}