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| 摘要: |
| 本文研究了赋权分数桥dXt=-α(Xt)/(T-t)dt+dBta,b,0≤t < T,中未知参数α>0的参数估计问题,其中Ba,b是参数为a>-1,|b|<1,|b|≤a+1的赋权分数布朗运动.假设对随机过程Xt进行离散观测ti=i△n,i=0,…,n,且Tn=n△n.本文构造了α的最小二乘估计αn,证明了当n→∞时,αn依概率收敛到α. |
| 关键词: 赋权分数桥 最小二乘估计 α-赋权分数桥 参数估计 |
| DOI： |
| 分类号:O211.6 |
| 基金项目:Supported by National Natural Science Foundation of China (11271020) and the Foundation for Young Talents in College of Anhui Province (2012SQRL170). |
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| PARAMETER ESTIMATION FOR α-WEIGHTED FRACTIONAL BRIDGE WITH DISCRETE OBSERVATIONS |
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GUAN Mei,YIN Xiu-wei
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| Abstract: |
| In this paper, we consider the problem of estimating the unknown parameter α>0 of the weighted fractional bridge dXt=-α(Xt)/(T-t)dt+dBta,b, 0≤t < T, where Ba,b is a weighted fractional Brownian motion of parameters a>-1,|b|<1,|b|≤a+1. Assume that the process is observed at discrete time ti=i△n, i=0,…, n and Tn=n△n, we construct a least squares estimator αn of α and prove that αn converges to α in probability as n→∞. |
| Key words: weighted fractional bridge least squares α-weighted fractional bridge parameter estimation estimator |
