Laplace approximation for rough differential equation driven by fractional Brownian motion

Abstract

We consider a rough differential equation indexed by a small parameter $\varepsilon>0$. When the rough differential equation is driven by fractional Brownian motion with Hurst parameter $H$ ($1/4<H<1/2$), we prove the Laplace-type asymptotics for the solution as the parameter $\varepsilon$ tends to zero.