0642596 20260213094704.220251204235959.9 105023670983 001633605300003 10.1007/s11118-025-10247-8 41 s. P cav_un_epca*02547750926-260164Springer Besov-Orlicz space Rough path Rough differential equation cav_un_auth*0356972 Čoupek P. CZ cav_un_auth*0494629 Hendrych F. CZ cav_un_auth*0370372 Slavík Jakub UTIA-B Stochastická informatika Department of Stochastic Informatics SI SI CZ Ústav teorie informace a automatizace AV ČR, v. v. i. https://library.utia.cas.cz/separaty/2025/SI/slavik-0642596.pdf GA22-12790S GA ČR CZ cav_un_auth*0449240 In the article, the rough path theory is extended to cover paths from the exponential Besov-Orlicz space, and the extension is used to treat nonlinear differential equations driven by such paths. The exponential Besov-Orlicz-type spaces, rough paths, and controlled rough paths are defined and analyzed, a sewing lemma for such paths is given, and the existence and uniqueness of the solution to differential equations driven by these paths is proved. The results cover equations driven by paths of continuous local martingales with Lipschitz continuous quadratic variation (e.g. the Wiener process) or by paths of fractionally filtered Hermite processes in the nth Wiener chaos with Hurst parameter H ∈ (1/3, 1/2] (e.g. the fractional Brownian motion). 2027 BA WOS 10000 10100 10101 RVO:67985556 https://hdl.handle.net/11104/0372942 cav_un_auth*0340903 Matematicko-fyzikalni fakulta UK MFF UK S 3 C https://arxiv.org/abs/2406.02793 MATHEMATICS 1 0.2 9.6 0.00289 0.847 1309 51 0.907 31.99 1.04 217 Q1 0.800 64 Q2 61 0.79 Q2 60.5 2026 105023670983 SCOPUS PUBMED 001633605300003 WOS cav_un_epca*0254775 Potential Analysis 64 1 2026 0926-2601 1572-929X Springer