Speaker

Bin Pei（JSPS、九州大学）

Title:

Averaging Principles for Mixed Fast-Slow Systems Driven by Fractional Brownian Motion

Abstract:

We focus on fast-slow systems involving both fractional Brownian motion (fBm) and standard Brownian motion (Bm). The integral with respect to Bm is the standard Ito integral, and the integral with respect to fBm is the generalised Riemann-Stieltjes integral using the tools of fractional calculus. 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 mean square sense, which is characterized by the solution of stochastic differential equations driven by fBm whose coefficients are averages with respect to the stationary measure of the fast-varying diffusion. This averaging principle paves the way for reduction of computational complexity. The implication is that one can ignore the complex original systems and concentrate on the average systems instead.(This is joint work with Yuzuru INAHAMA and Yong XU)