算子稳定随机向量序列的一些极限结果

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.

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

For sequences of R~d-valued random vectors with operator stable distribu- tion(without Gaussian component)with an exponent A,an invertible linear operator, this paper obtians the limiting results for the partial sums and weighted sums(inculd- ing 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 appli- cations,we obtain Chover-type laws of iterated logarithm for them under the spectral decomposition of A,which is related to the eigenvalues of A.