A generalized change of variable formula for the Young integral

Abstract

This article shows an Itô-Wentzell type formula adapted to Young integral. We apply this formula to study differential equations driven by α-Hölder paths with α∈121.We obtain a formula for the composition and the inverse of solution maps associated with a Young differential equation. Also, we prove a Leibniz rule for interchanging derivative and the Young integral, and a substitution formula for Young integrals.We also study the Cauchy problem for first-order semilinear differential equations driven by a Hölder path via the Method of Characteristics. We also prove a version of the structure theorem of characteristics in the Young context. We conclude by showing the explicit solution of a transport equation perturbed by the H-fractional Brownian motion with Hurst parameter 1/2 <H ≤ 1.