Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (5): 1945-1958.doi: 10.1016/S0252-9602(11)60373-1

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STABLE SUB-GAUSSIAN MODELS CONSTRUCTED BY POISSON PROCESSES

 DAI Hong-Shuai, LI Yu-Qiang*   

  1. Department of Mathematics, Central South University, Changsha 410075, China|School of Finance and Statistics, East China Normal University, Shanghai 200241, China
  • Received:2009-11-18 Revised:2010-10-26 Online:2011-09-20 Published:2011-09-20
  • Contact: LI Yu-Qiang,yqli@stat.ecnu.edu.cn E-mail:yqli@stat.ecnu.edu.cn
  • Supported by:

    The research supported by National Natural Science Foundation of China (10901054).

Abstract:

In this paper, we first prove that one-parameter standard -stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend this result to the two-parameter processes. At last, we consider the approximation of the subordinated fractional Brownian motion.

Key words: stable sub-Gaussian process, weak convergence, Poisson process, Riemann integral

CLC Number: 

  • 60F17
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