THE FUNCTIONAL CENTRAL LIMIT THEOREM AND WEAK CONVERGENCE TO STOCHASTIC INTEGRALS II
推导了分数积分过程（长记忆过程）部分和的函数中心极限定理，极限分布为分数布朗运动，并得到了分数被积函数与弱相依积分子的随机积分的弱收敛结果。
This paper derives a functional central limit theorem for the partial sums of fractionally integrated processes, otherwise known as I ( d ) processes for | d | < 1/2. Such processes have long memory, and the limit distribution is the so-called fractional Brownian motion, having correlated increments even asymptotically. The underlying shock variables may themselves exhibit quite general weak dependence by being near-epoch-dependent functions of mixing processes. Several weak convergence results for stochastic integrals having fractional integrands and weakly dependent integrators are also obtained. Taken together, these results permit I ( p + d ) integrands for any integer p ≥ 1.