Singularity of Subfractional Brownian Motions with Different Hurst Indices

We prove that the probability measures generated by two subfractional Brownian motions with different Hurst indices are singular with respect to each other.     

Chung’s law of the iterated logarithm for subfractional Brownian motion

Let X~H= {X~H(t), t ∈ R_+} be a subfractional Brownian motion in R~d. We provide a sufficient condition for a self-similar Gaussian process to be strongly locally nondeterministic and show that X~H has the property of strong local nondeterminism. Applying this property and a stochastic integral representation of X~H, we establish Chung's law of the iterated logarithm for X~H.     

$H<1/6$时次分数布朗运动赋权立变差的一个注记

本文中我们利用Malliavin计算的技巧研究了$H<1/6$时次分数布朗运动赋权立变差的$L^2$收敛性.