0638624 20260224162825.820250904235959.9 105007148009 001443918000001 10.3934/dcdsb.2025044 16 s. P cav_un_epca*02578451531-34923011 (2025)4296-4311AIMS Press Besov–Orlicz space rough path Young regime Hermite process 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-0638624.pdf https://www.aimsciences.org//article/doi/10.3934/dcdsb.2025044 GA22-12790S GA ČR CZ cav_un_auth*0449240 In the article, we consider nonlinear differential equations driven by paths from the exponential Besov–Orlicz space $B^\alpha_{\Phi_\beta,q}$ for $\alpha \in (1/2, 1)$, $\Phi_\beta(x) \sim e^{x^\beta} - 1$ with $\beta \in (0, \infty)$, and $q \in (0, \infty]$. By appealing to the recently obtained sewing lemma for such paths, we construct a Young-type integral and show that such equations admit a unique solution that is again of exponential Besov–Orlicz regularity. The results cover equations driven by paths of a large number of stochastic processes that exhibit long-range dependence, e.g. fractional Brownian motion with Hurst parameter $H \in (1/2, 1)$ or, more generally, any Hermite process. WOS BA 10000 10100 10101 2026 RVO:67985556 https://hdl.handle.net/11104/0370051 S C MATHEMATICS.APPLIED 1.3 0.1 6.2 0.00681 0.552 4181 65 0.735 36.02 1.33 1091 Q1 1.200 187 Q2 64 0.7 Q2 63.5 2025 105007148009 SCOPUS PUBMED 001443918000001 WOS cav_un_epca*0257845 Discrete and Continuous Dynamical Systems-Series B Roč. 30 č. 11 2025 4296 4311 1531-3492 1553-524X AIMS Press