分野別セミナー

This work focuses on a slow-fast system perturbed by mixed fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. The integral with respect to fractional Brownian motion is the generalized Riemann-Stieltjes integral and the integral with respect to Brownian motion is the standard Itô integral. We establish a large deviation principle with a good rate function for the slow component. Our approach is based on the variational framework and the weak convergence criteria for mixed fractional Brownian motion. By combining the weak convergence method and Khasminskii's averaging principle, we show that the controlled slow component weakly converges to a limits which is related to a unique invariant measure of the uncontrolled fast component. (Joint work with Prof. Yuzuru INAHAMA and Prof. Yong XU)