线性过程的大数定律与中心极限定理

Laws of large numbers and central limit theorems for linear process

设{Xt}是一个线性过程Xt=∑∞j=0cjεt-j,其中{cj}是常数列,{εi,Fi}是一个适应的鞅差序列,∑∞j=0cj2Eε2t-j<∞,t=1,2,….本文利用线性过程的Beveridge-Nelson分解,得到了一类线性过程的大数定律和中心极限定理,推广和改进了Philips和Solo文中的相应结果.

Let { Xt } be a linear process ： Xt=∞↑∑↓j=0 cjε（t-j） here {cj} is a nonrandom constants sequence,{εi,Fi} is an adapted martingale difference sequence, ∞↑∑↓j=0 c^2jeε^2（l-j）〈∞,t=1,2,…, We obtain laws of large numbers and central limit theorems of linear processes by using the Beveridge - Nelson decomposition about linear process, we generalizes and improves the corresponding results in Phillips and Solo.