{"paper":{"title":"Time evolution towards q-Gaussian stationary states through unified Ito-Stratonovich stochastic equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"B. Coutinho dos Santos, C. Tsallis","submitted_at":"2010-04-05T21:28:08Z","abstract_excerpt":"We consider a class of single-particle one-dimensional stochastic equations which include external field, additive and multiplicative noises. We use a parameter $\\theta \\in [0,1]$ which enables the unification of the traditional It\\^o and Stratonovich approaches, now recovered respectively as the $\\theta=0$ and $\\theta=1/2$ particular cases to derive the associated Fokker-Planck equation (FPE). These FPE is a {\\it linear} one, and its stationary state is given by a $q$-Gaussian distribution with $q = \\frac{\\tau + 2M (2 - \\theta)}{\\tau + 2M (1 - \\theta)}<3$, where $\\tau \\ge 0$ characterizes the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0722","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"}