【摘要】 设X={X(t),t∈RN+}为以d×d可逆矩阵B为指数的N指标Rd值算子稳定Lévy过程,讨论了X在R+N的子区域上的像集Hausdorff维数问题,证明了dim X([1,2]N)=min{d,αkN+sum from j=1 to k dj(1-αk/αj),k=1,…,p},a.s.,其中α1>α2>…>αp为B的p个不同的特征值实部的倒数,d1,…,dp分别为它们所对应子空间的维数.该结论表明X在R+N的子区域上像集Hausdorff维数完全由B的特征值的实部来确定.更多还原

【Abstract】 Let X={X(t),t∈RN+ }be a N-parameter operator stable Lévy process in Rd with exponent B,where B is a d×d invertible matrix.The Hausdorff dimension for the range of X on the region of RN+ is discussed.It is proved that dim X(N)=min{d,αkN+∑kj=1dj(1-αkαj),k=1,…,p},a.s., where α1>α2>…>αp are the reciprocal of the real parts of p different eigenvalues of B,and d1,…,dp are their dimensions of corresponding subspaces respectively.It indicates that the Hausdorff dimension for the range of X on the region of RN+ is completely determined by the real parts of B’s eigenvalues.更多还原