Asymptotic properties of MLE for partially observed fractional diffusion system with dependent noises

被引：9
作者：
Brouste, Alexandre [1 ]
机构：
[1] Univ Maine, Dept Math, F-72000 Le Mans 9, France
来源：
JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 2010年 / 140卷 / 02期
关键词：
Maximum likelihood estimation; Partially observed diffusion process; Continuous-time observations; DIFFERENTIAL-EQUATIONS DRIVEN;
D O I：
10.1016/j.jspi.2009.08.001
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
The paper studies long time asymptotic properties of the maximum likelihood estimator (MILE) for the signal drift parameter in a partially observed fractional diffusion system with dependent noise. Using the method of weak convergence of likelihoods due to Ibragimov and Khasminskii [1981. Statistics of Random Processes. Springer, New-York], consistency, asymptotic normality and convergence of the moments are established for MLE. The proof is based on Laplace transform computations which was introduced in Brouste and Kleptsyna [2008. Asymptotic properties of MLE for partially observed fractional diffusion system, preprint]. (C) 2009 Elsevier B.V. All rights reserved.
引用
收藏
页码：551 / 558
页数：8
相关论文
共 23 条
[1]  
[Anonymous], 2004, STAT INFERENCE ERGOD, DOI DOI 10.1007/978-1-4471-3866-2
[2]  
BERCU B, 2008, SHARP LARGE DEVIATIO
[3]  
BROUSTE A, 2008, ASYMPTOTIC PROPERTIE
[4]  
Cheridito P., 2003, Electron. J. Probab., V8, P1, DOI [10.1214/EJP.v8-125, DOI 10.1214/EJP.V8-125]
[5]  
Chigansky P., 2009, Statist. Inference Stoch. Processes, V12, P139, DOI DOI 10.1007/S11203-008-9025-4
[6]   Stochastic analysis, rough path analysis and fractional Brownian motions [J].
Coutin, L ;
Qian, ZM .
PROBABILITY THEORY AND RELATED FIELDS, 2002, 122 (01) :108-140
[7]  
Ibragimov I.A., 1981, Statistics of random processes
[8]  
JOST C, 2007, STOCHASTIC PROCESSES, V27, P514
[9]  
Kleptsyna M., 2002, Statistical Inference Stochastic Processes, V5, P249
[10]  
KLEPTSYNA M. L., 2002, STOCHASTICS INT J PR, V72, P229, DOI 10.1080/10451120290019203
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