{"paper":{"title":"Memory-Dependent FPK Equations for Nonlinear SDOF Oscillators Under Fractional Gaussian Noise Excitation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bin Pei, Lifang Feng, Yong Xu","submitted_at":"2025-10-23T01:59:31Z","abstract_excerpt":"This paper investigates the transient probabilistic responses of nonlinear single-degree-of-freedom oscillators subjected to external fractional Gaussian noise (FGN) excitation. Owing to the inherent long-range correlations and memory characteristics of FGN, the resulting response process exhibits non-Markovian properties, rendering the classical Fokker-Planck-Kolmogorov (FPK) equation method inapplicable in its direct form. To overcome this critical challenge, a memory-dependent FPK (memFPK) equation is formulated for two-dimensional nonlinear stochastic systems within the fractional Wick-It\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.20124","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.20124/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"}