分野別セミナー

Abstract:
This talk focuses on systems of two-times-scales stochastic partial differential equations. We establish an averaging principle in which the fast-varying diffusion process acts as a “noise” and is averaged out in the limit. The slow process is shown to have a limit in the L2 sense, which is characterized by the solution of a stochastic partial differential equation whose coefficients are averages of that of the original slow process with respect to the stationary measure of the fast-varying diffusion. This averaging principle paves a way for reduction of computational complexity. The implication is that one can ignore the complex original systems and concentrates on the average systems instead.