Some Random Process Limit Theorem

This paper is mainly concerned with the law of iterated logarithm with finite partial sum and the modulus of non-differentiability of the two-parameter Qrnstein-Uhlenbeck process. The paper consists of two chapters. In the first chapter , we consider the law of iterated logarithm with finite partial sum. Under certain condition ,we extend the law of iterated logarithm with finite partial sum for the Wiener process to Gaussian process ; In addition, we apply the law of iterated logarithm of Chung to the finite partial sum condition. In the second chapter , we consider the modulus of non-differentiability of the two-parameter Ornstein-Uhlenbeck process,we find the normalizing factor, and prove concerned theorems.