由鞅差所产生的非平稳线性过程的随机泛函中心极限定理

在非平稳条件下, 证明了{ξ_n(t); 0≤t≤1}的所有有限维分布在条件概率PB(·)下均弱收敛到Wiener过程W的有限维分布, 进而得到随机指标和过程{ξ_νn(u);0≤u≤1}弱收敛于Wiener过程W, 其中{ν_n;n∈N}是一列满足一定条件的正整数随机变量.

A Functional Central Limit Theorem for the Random Sum of Linear Process of Martingale Differences

Under some nonstationary conditions, it is proved that all the finite dimensional distributions of the stochastic process {ξ_n(t); 0≤t≤1} weakly converge to the finite dimensional distribution of the Wiener measure under the conditional probability measure PB(·). At last, it is proved that the process {ξ_νn(u);0≤u≤1} weakly converges to the Wiener measure, where {ν_n;n∈N} is a sequence of positive integer-valued random variables statisfying some conditions.