算子稳定随机向量序列的一些极限结果

Some Limiting Results for Sequences of Random Vectors with Operator Stable Law

对于独立同分布的没有Gauss分量的指数为可逆线性算子A的算子稳定的R^d值随机向量序列,本文通过积分检验讨论了其部分和及加权和(包括一些经典的加权和,如Cesàro加权和,后置和方式,Euler可和方式,Borel可和方式,几何加权和等)的极限结果.由此得到了部分和及加权和在相对于A的谱分解下的Chover型重对数律,这是与A的特征值的实部有关的结果.

For sequences of R^d-valued random vectors with operator stable distribution （without Gaussian component） with an exponent A, an invertible linear operator, this paper obtians the limiting results for the partial sums and weighted sums （inculding some classical summable methods, such as Cesàro＇s method, delayed sum, Euler＇s method, Borel＇s method and geometrical weighted sum, etc.） via integer test. As applications, we obtain Chover-type laws of iterated logarithm for them under the spectral decomposition of A, which is related to the eigenvalues of A.