{"paper":{"title":"Fractional Cox--Ingersoll--Ross process with non-zero <<mean>>","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anton Yurchenko-Tytarenko, Yuliya Mishura","submitted_at":"2018-04-05T05:49:20Z","abstract_excerpt":"In this paper we define the fractional Cox-Ingersoll-Ross process as $X_t:=Y_t^2\\mathbf{1}_{\\{t<\\inf\\{s>0:Y_s=0\\}\\}}$, where the process $Y=\\{Y_t,t\\ge0\\}$ satisfies the SDE of the form $dY_t=\\frac{1}{2}(\\frac{k}{Y_t}-aY_t)dt+\\frac{\\sigma}{2}dB_t^H$, $\\{B^H_t,t\\ge0\\}$ is a fractional Brownian motion with an arbitrary Hurst parameter $H\\in(0,1)$. We prove that $X_t$ satisfies the stochastic differential equation of the form $dX_t=(k-aX_t)dt+\\sigma\\sqrt{X_t}\\circ dB_t^H$, where the integral with respect to fractional Brownian motion is considered as the pathwise Stratonovich integral. We also sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01677","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"}