Some Differential Systems Driven by a fBm with Hurst Parameter Greater than 1/4

This note is devoted to show how to push forward the algebraic integration setting in order to treat differential systems driven by a noisy input with Holder regularity greater than \(1/4\). After recalling how to treat the case of ordinary stochastic differential equations, we mainly focus on the case of delay equations. A careful analysis is then performed in order to show that a fractional Brownian motion with Hurst parameter H > 1 ∕ 4 fulfills the assumptions of our abstract theorems.