双分数Brown运动的连续模和不可微模  

Continuity moduli and non-differentiability moduli for bifractional Brownian motion

作　　者：王文胜 Wen she ng Wang

机构地区：[1]杭州电子科技大学经济学院

出　　处：《中国科学：数学》2019年第9期1209-1224,共16页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11671115)资助项目

摘　　要：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.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.

关 键 词：自相似Gauss过程 双分数Brown运动 小球概率 连续模 不可微模 局部时 

分 类 号：G15[文化科学] G17