摘要
Let W={W(t);t ∈R_+~N} be the d-dimensional N-parameter Brownian Sheet. Sufficient conditions for a compact set F C Rd \ {0} to be a polar set for W are proved. It is also proved that if 2N≤d, then for any compact set E (?)R_>~N ,inf {dimF : F ∈B(Rd), P{W(E) ∩F≠(?)}>0} = d- 2DiroE, and if 2N > d, then for any compact set F C Rd \ {0}, inf{dim E : E ∈ B(R_>~N), P{W(E)∩F≠(?)}>0}=d/2-DimF/2,where B(Rd) and B(R_>~N) denote the Borel σ-algebra in Rd and R_>~N respectively, and dim and Dim are Hausdorff dimension and Packing dimension respectively.
Let W={W(t);t ∈R_+~N} be the d-dimensional N-parameter Brownian Sheet. Sufficient conditions for a compact set F C Rd \ {0} to be a polar set for W are proved. It is also proved that if 2N≤d, then for any compact set E (?)R_>~N ,inf {dimF : F ∈B(Rd), P{W(E) ∩F≠(?)}>0} = d- 2DiroE, and if 2N > d, then for any compact set F C Rd \ {0}, inf{dim E : E ∈ B(R_>~N), P{W(E)∩F≠(?)}>0}=d/2-DimF/2,where B(Rd) and B(R_>~N) denote the Borel σ-algebra in Rd and R_>~N respectively, and dim and Dim are Hausdorff dimension and Packing dimension respectively.
基金
Supported by Sci-tech Innovation Project of Educational Department of Hubei Province
Major Project of Educational Department of Hubei Province (2003A005).
