次分数布朗运动的几点注记

Remarks on sub-fractional Brownian motion

假设SH={StH,t≥0}是指标为H∈(0,1)的次分数Brown运动,证明了当h→+∞时,增量过程(ShH+t-SHh,t≥0)依分布收敛于指数H的分数Brown运动,同时讨论了与次分数Brown噪声相关联的极限定理。

Let SH={SHt,t≥0} be a sub-fractional Brownian motion with index H∈（0,1）.It is shown that the increment process generated by the sub-fractional Brownian motion（SHh＋t-SHh,t≥0） converges to a fractional Brownian motion with Hurst index H in the sense of finite dimensional distributions,as h tends to infinity.Also,the limit theorems associated with the subfractional Brownian noise are also studied.