{"paper":{"title":"Higher-order Derivative Local Time for Fractional Ornstein-Uhlenbeck Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jingjun Guo, Yanping Xiao","submitted_at":"2018-10-30T14:31:30Z","abstract_excerpt":"In this article, existence of the $k$-th order derivatives of local time $ \\widehat{\\alpha}^{(k)}(x,t)$ is considered for two d-dimensional fractional Ornstein-Uhlenbeck processes $X^{H_1}_t$ and $\\widetilde{X}^{H_2}_s$ with Hurst parameters $H_1$ and $H_2$, respectively. Moreover, H$\\hat{o}$lder regularity condition of fractional Ornstein-Uhlenbeck process $X^{H}_t$ of local time $\\tilde{\\alpha}^{(k)}(x,t)$ is obtained by some techniques using in Guo et al. (2017) and in Lou et al. (2017)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12772","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"}