The exact Hausdorff measures for the graph and image of a multidimensional iterated Brownian motion  

作　　者：Rong-mao ZHANG Zheng-yan LIN 

机构地区：[1]Department of Mathematics,Zhejiang University,Hangzhou 310027,China

出　　处：《Science China Mathematics》2007年第1期35-46,共12页中国科学：数学（英文版）

基　　金：This work was partially supported by the National Natural Science Foundation of China (Grant No. 10131040);China Postdoctoral Science Foundation.

摘　　要：Let {W (t), t ∈ R}, {B(t), t ∈ R +} be two independent Brownian motions on R with W(0) = B(0) = 0. In this paper, we shall consider the exact Hausdorff measures for the image and graph sets of the d-dimensional iterated Brownian motion X(t), where X(t) = (X 1(t),…, X d (t)) and X 1(t),…, X d (t) are d independent copies of Y(t) = W(B(t)). In particular, for any Borel set Q ? (0, ∞), the exact Hausdorff measures of the image X(Q) = {X(t): t ∈ Q} and the graph GrX(Q) = {(t, X(t)): t ∈ Q} are established.Let {W(t),t∈R}, {B(t),t∈R+} be two independent Brownian motions on R with W(0) = B(0) = 0. In this paper, we shall consider the exact Hausdorff measures for the image and graph sets of the d-dimensional iterated Brownian motion X(t), where X(t) = (Xi(t),... ,Xd(t)) and X1(t),... ,Xd(t) are d independent copies of Y(t) = W(B(t)). In particular, for any Borel set Q (?) (0,∞), the exact Hausdorff measures of the image X(Q) = {X(t) : t∈Q} and the graph GrX(Q) = {(t, X(t)) :t∈Q}are established.

关 键 词：GRAPH Hausdorff measure IMAGE iterated Brownian motion sojourn time 60F15 60G15 60G17 

分 类 号：O157.5[理学—数学]