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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2017, Vol. 32 Issue (3): 295-305    DOI:
    
On estimations for the parameters of fractional diffusion models and their applications
SUN Xiao-xia1 , SHI Yin-hui2
1. School of Mathematics, Dongbei University of Finance and Economics, Dalian 116025, China
2. School of Mathematics, Jiangsu Normal University, Xuzhou 221116, China
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Abstract  In this paper, the estimations for the parameters of fractional diffusion models and their applications are presented. Fractional diffusion models satisfy the stochastic differential equations driven by fractional Brownian motions. The paper’s main results are: (1) An estimator for the diffusion parameter by the method of quadratic variation and estimators for the drift parameters by least squares method are given; (2) These estimators are proved to be strong consistent and asymptotically normal; (3) These estimators are examined via the MCMC method and applied to empirical data of SHIBOR.

Key words： fractional Brownian motion      the least squared estimators      strong consistent      asymptotically normal      
Received: 21 December 2016      Published: 07 April 2018
CLC:  O211.64  
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SUN Xiao-xia , SHI Yin-hui. On estimations for the parameters of fractional diffusion models and their applications. Applied Mathematics A Journal of Chinese Universities, 2017, 32(3): 295-305.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2017/V32/I3/295


分数扩散模型的参数估计及其应用

研究分数扩散模型的参数估计及其应用问题. 分数扩散模型是一类由分数Brownian运动驱动的随机微分方程. 主要结果有: (1) 利用二次变差方法给出模型中扩散系数的估计量, 通过最小二乘法给出模型中漂移系数的估计量; (2) 证明这些估计量的一致收敛性和渐近正态性; (3) 利用MCMC方法对此估计量进行验证, 并通过R软件将上述模型以及参数估计量应用到SHIBOR利率中进行实证研究.

关键词： 分数Brownian运动,  最小二乘估计量,  一致收敛性,  渐近正态性 
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