分野別セミナー

This work concerns the large deviation principle for a family of slow-fast systems perturbed by infinite-dimensional mixed fractional Brownian motion with Hurst parameter H (1/2<=H<1). We employ the weak convergence method which is based on the variational representation formula for infinite-dimensional mixed fractional Brownian motion. To obtain the weak convergence of the controlled systems, we apply Khasminskii's time discretization technique. In addition, we drop the boundedness assumption of the drift coefficients of the slow components and the diffusion coefficients of the fast components. Finally, the moderate deviation principle for the slow-fast systems is derived as a consequence of the proposed large deviation principle. Joint work with Prof. Yong XU, Dr. Xiaoyu Yang and Prof. Bin PEI (arXiv:2410.21785v2).