Sample path properties of bifractional Brownian motion
Sample path properties of bifractional Brownian motion
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DOI：
10.3150/07-bej6110
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发表时间：
2007-11-01
期刊：
影响因子：
1.5
通讯作者：
Xiao, Yimin
中科院分区：
文献类型：
--
作者：
Tudor, Ciprian A.;Xiao, Yimin
设B-H，B-K = {B-H，B-K（t），t是R ~+的元素}是R-d中的双分式布朗运动.我们证明了B-H，B-K是强局部非确定的。利用这一性质和B-H，B-K的随机积分表示，我们建立了B-H，B-K的Chung重对数律，以及B-H，B-K的局部时的尖锐保持器条件和尾概率估计.我们还考虑了棒上多参数双分式布朗运动B-（H），棒上B-（K）= {B-（H）over棒，B-（K）在bar（t）上，t是R-+（N）}在R-d中的元素.
Let B-H,B-K = {B-H,B-K(t), t is an element of R+} be a bifractional Brownian motion in R-d. We prove that B-H,B-K is strongly locally non-deterministic. Applying this property and a stochastic integral representation of B-H,B-K, we establish Chung's law of the iterated logarithm for B-H,B-K, as well as sharp Holder conditions and tail probability estimates for the local times of B-H,B-K.We also consider the existence and regularity of the local times of the multiparameter bifractional Brownian motion B-(H) over bar,B-(K) over bar = {B-(H) over bar,B-(K) over bar(t), t is an element of R-+(N)} in R-d using the Wiener-Ito chaos expansion.