论文标题
在快速慢系统的最佳时刻假设下进行确定性均质化。第1部分
Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 1
论文作者
论文摘要
我们考虑对形式的多尺度系统的确定性均质化（收敛到随机微分方程） x_{k+1} = x_k + n^{-1} a_n(x_k,y_k) + n^{-1/2} b_n(x_k,y_k), \quad y_{k+1} = T_n y_k, \] where the fast dynamics is given by a family $T_n$ of nonuniformly expanding maps.第1部分是基于我们最近的关于不均匀扩展地图家庭的Martingale近似工作的工作。我们证明了一个迭代的弱不变性原理，并为此类地图建立了最佳的迭代力矩界限。 （即使对于固定的不均匀扩展的地图t，迭代的力矩边界也是新的。）均质化结果是奇异果，Friz，Friz，Korepanov，Melbourne＆Zhang在Rough Path Theory中的平行发展的结果。
We consider deterministic homogenization (convergence to a stochastic differential equation) for multiscale systems of the form \[ x_{k+1} = x_k + n^{-1} a_n(x_k,y_k) + n^{-1/2} b_n(x_k,y_k), \quad y_{k+1} = T_n y_k, \] where the fast dynamics is given by a family $T_n$ of nonuniformly expanding maps. Part 1 builds on our recent work on martingale approximations for families of nonuniformly expanding maps. We prove an iterated weak invariance principle and establish optimal iterated moment bounds for such maps. (The iterated moment bounds are new even for a fixed nonuniformly expanding map T.) The homogenization results are a consequence of this together with parallel developments on rough path theory in Part 2 by Chevyrev, Friz, Korepanov, Melbourne & Zhang.
