J4 ›› 2011, Vol. 46 ›› Issue (3): 102-108.

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Remarks on sub-fractional Brownian motion

SHEN Guang-jun 1,2, HE Kun 3, YAN Li-tan 3*   

  1. 1. Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China;
    2. Department of Mathematics, Anhui Normal University, Wuhu 241000, Anhui, China;
    3. Department of Mathematics, Donghua University, Shanghai 201620, China
  • Received:2010-05-06 Published:2011-04-21

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Abstract:

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.

Key words: Brownian motion; fractional Brownian motion; sub-fractional Brownian motion; quasi-Dirichlet process

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