601 Pao Yue-Kong Library
The generalized Langevin equation (GLE) with fraction noise has been used widely by biologists and physists to explain some abnormal diffusion behaviors. We consider the generalized Langevin equation with fractional noise in the overdamped regime, which naturally gives the fractional stochastic differential equations (FSDE). In the FSDE, the Caputo fractional derivative and fractional noise are related by fluctuation dissipation theorem. We first investigate the FSDE in theory and show the well-posedness. In the case the force is linear, we can show that the overdampled GLE converges to Gibbs measure in algebraic rate. Since the ergodicity for general potential is unclear, we then investigate this by designing a fast numerical scheme for sampling the overdamped Langevin equation. This talk is based on joint works with Jian-Guo Liu (Duke), Jianfeng Lu (Duke) and Di Fang (UW-Madison).