The linear self-attracting diffusion driven by the weighted-fractional Brownian motionⅡ:The parameter estimation  

作　　者：Litan Yan Rui Guo Wenyi Pei 

机构地区：[1]Department of Statistics,College of Science,Donghua University,Shanghai 201620,China [2]School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018,China

出　　处：《Science China Mathematics》2025年第4期939-968,共30页中国科学(数学英文版)

基　　金：supported by National Natural Science Foundation of China(Grant No.11971101)。

摘　　要：Let B^(a,b)be a weighted-fractional Brownian motion with Hurst indices a and b such that a>-1 and 0≤b<1∧(1+a).In this paper,we consider the linear self-attracting diffusion dX_(t)^(a,b)=dB_(t)^(a,b)−θ(∫t 0(X_(t)^(a,b)−X_(s)^(a,b))ds)dt+νdt with X_(0)^(a,b),whereθ>0 andν∈R are two real parameters.The model is an analog of the linear selfinteracting diffusion(see Cranston and Le Jan(1995)).Under the continuous observation,we study asymptotic behaviors of the least squares estimatorsθˆT andνˆT.In particular,when b>1/2,we obtain a new random variable Z_(1)^(a,b)which is called the Rosenblatt random variable if a=0,and we show that C_(a,b)T^(2-2b)(θ_(T)-θ)converges in distribution to the sum of the chi-square random variable with 1 degree of freedom and the random variable Z_(1)^(a,b).

关 键 词：weighted fractional Brownian motion Malliavin calculus self-attracting diffusion least squares estimation CONSISTENCY asymptotic distribution 

分 类 号：O211.6[理学—概率论与数理统计]