Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (3): 975-992.doi: 10.1016/S0252-9602(10)60095-1

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CONVERGENCE RATE OF AN APPROXIMATION TO MULTIPLE INTEGRAL OF FBM

 HU Yao-Zhong, WANG Bao-Bin   

  1. Department of Mathematics\thinspace, |University of Kansas 405 Snow Hall, Lawrence, Kansas 66045-2142, USA|Wuhan Institute of Physics and Mathematics, Chinese Academy of Science, Wuhan 430071, China|Graduate School of the Chinese Academy of Science, Beijing 100039, China
  • Received:2008-04-26 Online:2010-05-20 Published:2010-05-20
  • Supported by:

    This work is partially supported by NNSF of China (60534080) and the first author is supported in part by the National Science Foundation (DMS0504783)

Abstract:

In this article, we study the rate of convergence of the polygonal approximation to multiple stochastic integral Sp(f) of fractional Brownian motion of Hurst parameter H<1/2 when the fractional Brownian motion is replaced by its polygonal approximation. Under different conditions on f and for different p, we obtain different rates.

Key words: Fractional Brownian motion, multiple integral, stratonovich integral, convergence rate

CLC Number: 

  • 60G15
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