算子自相似马氏过程的Hausdorff维数定理

摘要

Let X(t)(t∈R+) be an isotropic, operator-self-similar Markov process, the Hausdorff dimension of the image, graph of X(t) are obtained under certain mild conditions, which show that the Hausdorff dimension can be estimated by the real parts of the eigenvalues of the self-similar exponent D.%对各向同性,算子自相似马氏过程,本文在恰当的条件下得到了其象集与图集的Hausdorff维数.其证明表明该维数的估计与其算子特征值的实部有关.