函数空间弱收敛与随机过程依分布收敛

ON WEAK CONVERGENCE AND CONVERGENCE OF STOCHASTIC PROCESSES IN DISTRIBUTION

设ξ_n(n=1,2,…)为一列随机过程,它的有限维分布收敛。本文用迫近法给出ξ_n依分布收敛的准则.

This paper uses an approximate method to obtain some conditions in which the stochastic processes ξn converge to ξ in distribution. It is a new and uniform method for studying convergence of stochastic processes in distribution. The main result is Theorem 1 . By applying this theorem to C [0,1]and D[0, 1] , some findings have been made.