For the N-parameter d-dimensional Generalized Brownian Sheet (in short G. B. S.) satisfying some conditions, this paper proves that when 2N≤αd, with probability one, E∈B(R_+~N), there holds 2/βdim E+2N-2Nβ/α≤d...For the N-parameter d-dimensional Generalized Brownian Sheet (in short G. B. S.) satisfying some conditions, this paper proves that when 2N≤αd, with probability one, E∈B(R_+~N), there holds 2/βdim E+2N-2Nβ/α≤dim (E)≤2/αdim E. Especially when α=β=1, we have dim (E)=2 dim E. Noting that even if α=β=1, the G. B. S. is wider than the Brownian Sheet, thus we have extended the uniform dimension result of Mountford, T,S.展开更多
基金Supported by the National Natural Science Foundation of China
文摘For the N-parameter d-dimensional Generalized Brownian Sheet (in short G. B. S.) satisfying some conditions, this paper proves that when 2N≤αd, with probability one, E∈B(R_+~N), there holds 2/βdim E+2N-2Nβ/α≤dim (E)≤2/αdim E. Especially when α=β=1, we have dim (E)=2 dim E. Noting that even if α=β=1, the G. B. S. is wider than the Brownian Sheet, thus we have extended the uniform dimension result of Mountford, T,S.
