α-混合随机场的弱收敛

Weak Convergence for α-mixing Random Fields

本文把Ｈｅｒｒｎｄｏｒｆ（１９８５）关于α－混合序列弱收敛的一个一般的充分条件拓广于α－混合随机场｛Ｘ＿ｔ，ｔ∈Ｚ￣ｄ｝，给出了｛Ｘ＿ｔ｝的部分和弱收敛于标准Ｂｒｏｗｎ单的一个充分条件，包含了现有的许多结果．

Hermdorf (1985 ) gave a general sufficient condition of weak convergence for α- mixing sequence.Inthis article, we extended which to an α- mixing random field {Xt,t∈ Z￣d}. Denote J_n= [1,n]￣d,S_n=be a convex function with g(0)=0,g(x )/x￣2 is non-decreasing and DenoteWe proved the following theorem:Theorem. Let {Xt,t ∈ Z￣d} be an α- mixing random field with EXt= 0,EXl < ∞,ifThen W_n weakly converge to a standard Brownian sheet W.