NONLINEAR FUNCTIONS AND CONVERGENCE TO BROWNIAN MOTION: BEYOND THE CONTINUOUS MAPPING THEOREM
研究了满足泛函中心极限定理的离散时间随机过程样本均值的弱收敛性，将Park和Phillips(1999)及de Jong(2002)的结果推广到更广泛的函数类，如所有局部可积函数。
Weak convergence results for sample averages of nonlinear functions of (discrete-time) stochastic processes satisfying a functional central limit theorem (e.g., integrated processes) are given. These results substantially extend recent work by Park and Phillips (1999, Econometric Theory 15, 269–298) and de Jong (2002, working paper), in that a much wider class of functions is covered. For example, some of the results hold for the class of all locally integrable functions, thus avoiding any of the various regularity conditions imposed on the functions in Park and Phillips (1999) or de Jong (2002).I thank Robert de Jong for drawing my attention to this problem and Hannes Leeb for helpful comments. This paper was presented at the Econometric Society European Meeting 2002 in Venice.