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.