【摘要】 设B（t）=（B（t））=（B₁（t）,B₂（t）,…,B_N（t））为N维Brown运动,设α（x）= (α_ij（x）,1■i■d,1■j■N),β（x）=（β_i（x）,1■i■d）,x∈R^d,1■d■N,α（x）和β（x）有界连续和满足Lipchitz条件,且存在常数c₀>0,使得对每个x∈R^d,a（x）=α（x）α（x）^*的每个特征根都不小于c₀.设dX（t）=α（X（t））dB（t）+β（X（t））dt,设d■3.可以证明P（ω:DimX（E,ω）=DimGRX（E,ω）=2DimE,■E∈β[0,∞）)=1这里X（E,ω）={X（t,ω）:t∈E},GRX（E,ω）={（t,X（t,ω））:t∈E},DimF表示F的Packing维数.更多还原

【Abstract】 Let X（t）=X（O）+∫₀^tα（X（s））dB（s）+∫_o^tβ（X（s））ds be a d-dimensional non- degenerate diffusion processes,where B（t）is a Brownian Motion.Ifα（x）andβ（x）are bounded continuous and satisfy Lipschitz conditions on R^d,and a（x）=α（x）α（x）^* is uniformly positive definite,that is,for some positive constant co such that a（x）■c₀I_d×d,for all x E R^d,then we prove that when d■3,one have P（ω:DimX（E,ω）= DimGRX（E,ω）=2DimE,■E∈B[0,∞）)=1 where DimF denote the Packing dimension of F for F■R^l（l■1）,and X（E,ω）={X（t,ω）: t∈E},GRX（E,ω）={（t,X（t,ω））:t∈E},ω∈Ω.更多还原