带上循环扩散随机游动极限定理的构造性方法
Constructive approach to limit theorems for recurrent diffusive random walks on a strip
摘要：
考虑带上的常返扩散随机游动。给出了有限子域上格林函数的构造性条件，该条件包含一个具有多项式误差界的中心极限定理，一个局部极限定理，以及从粒子过程的角度考虑的混合环境.我们的条件可以被验证为广泛的一类环境，包括独立的环境，准周期环境，以及在无穷远渐近常数的环境。所提出的条件处理一个固定的环境，特别是，没有平稳性条件。
英文摘要：
We consider recurrent diffusive random walks on a strip. We present constructive conditions on Green functions of finite sub-domains which imply a Central Limit Theorem with polynomial error bound, a Local Limit Theorem, and mixing of environment viewed by the particle process. Our conditions can be verified for a wide class of environments including independent environments, quasiperiodic environments, and environments which are asymptotically constant at infinity. The conditions presented deal with a fixed environment, in particular, no stationarity conditions are imposed.
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