OU过程无穷级数在L_2-模下的重对数律与Chung-重对数律

THE LIL AND THE CHUNG-LIL FOR INFINITE SERIES OF INDEPENDENT OU PROCESSES UNDER L_2-NORM

设{X_k(t),-∞<t<∞} 为列相互独立的Ornstein-Uhlenbeoh过程,{X(t)=sum from n=1 to ∞ X_k(t),-∞<t<∞}为其无穷级数。本文讨论了{X（t）,-∞<t<∞}在L_2-模下的极限性质,得到了与Wiener过程相似的重对数律与Chung-重对数律。

Let {Xk(t), - ∞<t<∞}k=1∞ be a sequence of independent Ornetein-Uhlenbechprocesses, X(t) =∑Xk(t)> - ∞<t<∞. We establish the law of the iterated logarithm and the Chung type law of the iterated logarithm for {X(t), - ∞<t<∞} under L2-Norm, respectively.