N参数d维广义OU过程象集代数和的Hausdorff维数(英文)

ON THE HAUSDORFF DIMENSION OF ALGEBRAIC SUM OF THE IMAGE SETS FOR GOUP_N^d

设X(t)∶RN+→Rd是N参数d维广义OU过程.对任意的紧集E,F RN+\{0},考虑了X(t)象集代数和X(E)-X(F)的Hausdorff维数,得到了象集代数和Hausdorff维数的上下界,这些结果包含了Browniansheet和广义Browniansheet的相应结论.

Let X(t)∶R^N_+→R^d be GOUP^d_N.For any compact sets E,FR^N_+\｛0｝,the Hausdorff dimension of the algebraic sum of the image sets of X(E)-X(F) for X is considered in this paper.This result contains the corresponding one of Brownian sheet and generalized Brownian sheet.