长程相依过程关于矩完全收敛的精确渐近性质

Precise asymptotics for complete moment convergence of long memory processes

令X_t=∑_(k=0)~∞a_kε_(t-k)为一滑动平均过程,其中ε_k为均值为零的独立同分布随机变量序列,{a_k,k≥0}为满足条件a_k～k^(-α)l(k)的实数序列,其中l(k)为缓变函数.当1/2<α<1时,X_t为一长程相依过程,如分数积分过程等.该文得到了长程相依过程X_t关于一类矩完全收敛的精确渐近性质,此结果可直接得到X_t完全收敛的精确渐近性质.

Let Xt be a moving-average process defined byXt=∑k=0^∞0αkεt-k where the inno- vation ek is a sequence of i.i.d, random variables with mean zero. {αk,K≥0} is a sequence of real numbers with conditionαk-K^-al（k）which guarantees X~ becoming a long memory process when 1/2〈α〈1, such as the fractional Gaussian noise process and fractional process. Some results about precise asymptotics for a kind of complete moment convergence, which include complete convergence as a special case for long memorv process Xt are obtained.