双分数Brown运动的连续模和不可微模

令H∈(0,1)和K∈(0,1]是两个常数.设B^H,K={B^H,K(t),t∈R+}是R^d上指标为H和K的双分数Brown运动.本文证明BH,K的整体和局部连续模定理,并通过证明BH,K的小球常数存在,来证明B^H,K的不可微模定理.上述结果表明双分数Brown运动的样本函数是几乎处处连续和几乎处处不可微的.作为不可微模定理的一个应用,本文证明Tudor和Xiao(2008)关于双分数Brown运动的最大值局部时的一致Holder条件是最优的.

Continuity moduli and non-differentiability moduli for bifractional Brownian motion

Let B^H,K= {B^H,K(t), t ∈ R+} be a bifractional Brownian motion with indices H ∈(0, 1) and K ∈(0, 1] in Rd. We establish the global and local moduli of continuity for B^H,K. By proving the existence of the small ball constants for B^H,K, we establish the moduli of non-differentiability for BH,K. These results confirm that almost all sample functions of bifractional Brownian motion are continuous and nowhere differentiability.As an application of the modulus of non-differentiability, we prove that the uniform H?lder condition for the maximum local times of bifractional Brownian motion obtained in Tudor and Xiao(2008) is optimal.