Nonlinear Young integrals and differential systems in Hölder media

Yaozhong Hu, Khoa N. Lê

For Hölder continuous functions $W(t,x)$ and ${\varphi }_t$, we define nonlinear integral ${\int }_a^{b}W(dt,{\varphi }_t)$ in various senses, including Itô-Skorohod and pathwise. We study their proper…