A Weak Convergence to Rosenblatt Process

作者:SUN Xi chao YAN Li tan WANG Zhi College of Information Science and Technology Donghua University Shanghai China Department of Mathematics and Physics Bengbu College Bengbu China College of Science Donghua University Shanghai China
来源:Journal of Dong Hua University (english Edition), 2012, (06): 480-483.

摘要

A special approximation to Rosenblatt process with the finite-time interval representation was obtained. The construction of approximation family was based on the Poisson process. The proof to the approximation was divided into two aspects. Firstly, the approximation family was tight using the methods given by Billingsley; secondly, the finite-dimension distributions of approximation family converged weakly to the Rosenblatt process by proving the convergence of the corresponding characteristic functions.