论文标题
由分数布朗运动驱动的混合快速系统的平均原理
Averaging Principles for Mixed Fast-Slow Systems Driven by Fractional Brownian Motion
论文作者
论文摘要
我们专注于涉及分数布朗运动（FBM）和标准布朗运动（BM）的快速慢系统。相对于BM的积分是标准ITO积分，而相对于FBM的积分是使用分数演算工具的广义Riemann-Stieltjes积分。一个平均原理，其中快速慢系统的快速变化扩散过程是在极限中平均的噪声。结果表明，慢速过程在均等意义上具有限制，其特征在于由FBM驱动的随机微分方程的解，其系数相对于快速变化的扩散的固定度量平均。这意味着人们可以忽略复杂的原始系统，而是专注于平均系统。这种平均原理为降低计算复杂性铺平了道路。
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. An averaging principle in which the fast-varying diffusion process of the fast-slow systems acts as a noise to be averaged out in the limit is established. It is shown that the slow process has a limit in the mean square sense, which is characterized by the solution of stochastic differential equations driven by fBm whose coefficients are averaged with respect to the stationary measure of the fast-varying diffusion. The implication is that one can ignore the complex original systems and concentrate on the averaged systems instead. This averaging principle paves the way for reduction of computational complexity.
