Nonstandard limit theorem for infinite variance functionals
Nonstandard limit theorem for infinite variance functionals
复制标题
无限方差泛函的非标准极限定理
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
C. Heyde
中科院分区：
文献类型：
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作者：
A. Sly;C. Heyde
研究了具有无穷方差的长程相依高斯序列的泛函，得到了非标准极限定理。当长程相关性足够强时，极限是Hermite过程，而当长程相关性较弱时，极限是α稳定的Levy运动.对于长程相关参数的临界值，极限是一个Hermite过程和α稳定Levy运动之和.
We consider functionals of long-range dependent Gaussian sequences with infinite variance and obtain nonstandard limit theorems. When the long-range dependence is strong enough, the limit is a Hermite process, while for weaker long-range dependence, the limit is α-stable Levy motion. For the critical value of the long-range dependence parameter, the limit is a sum of a Hermite process and α-stable Levy motion.