离散时间观测下的α-赋权分数桥的参数估计（英文）  

PARAMETER ESTIMATION FOR α-WEIGHTED FRACTIONAL BRIDGE WITH DISCRETE OBSERVATIONS

作　　者：管梅[1] 尹修伟 

机构地区：[1]合肥学院数学物理系,安徽合肥230601 [2]安徽师范大学数学系,安徽芜湖241000

出　　处：《数学杂志》2016年第1期87-99,共13页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(11271020);the Foundation for Young Talents in College of Anhui Province(2012SQRL170)

摘　　要：本文研究了赋权分数桥dX_t=-α(X_t/T-t)dt+dB_t^(a,b),0≤t<T,中未知参数α>0的参数估计问题.其中B^(a,b)是参数为a>-1.|b|<1,|b|≤a+1的赋权分数布朗运动.似设对随机过程X_t进行离散观测t_i=i△_n,i=0,…,n,且T_n=n△_n.本文构造了α的最小二乘估计α_n.证明了当n→∞时,α_n依概率收敛到α.In this paper,we consider the problem of estimating the unknown parameterα〉0 of the weighted fractional bridge dXt=-α（Xt/T-t）dt＋dBt^a,b,0≤tT,where B^a,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→∞.

关 键 词：赋权分数桥 最小二乘估计 α-赋权分数桥 参数估计 

分 类 号：O211.6[理学—概率论与数理统计]