Parameter Estimation and Optimal Filtering for Fractional Type Stochastic Systems

被引：35
作者：
M.L. Kleptsyna
A. Le Breton
M.-C. Roubaud
机构：
[1] Institute of Information Transmission Problems,Laboratoire de Modélisation et Calcul
[2] Université J. Fourier,LATP/ INRIA
[3] Université J. Fourier,undefined
来源：
Statistical Inference for Stochastic Processes | 2000年 / 3卷 / 1-2期
关键词：
fractional Brownian motion; innovation process; Girsanov formula; maximum likelihood; optimal filtering;
D O I：
10.1023/A:1009923431187
中图分类号：
学科分类号：
摘要：
Stochastic systems driven by fractional Brownian motions are investigated. At first analogs of the usual representation theorems and Girsanov's formula are derived. Then the tools are applied to solve some statistical problems of parameter estimation and optimal filtering.
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页码：173 / 182
页数：9
相关论文
共 17 条
[1]  
Coutin L.(1999)Abstract nonlinear filtering theory in the presence of fractional Brownian motion Ann. of Appl. Probab. 9 1058-1090
[2]  
Decreusefond L.(1999)Stochastic analysis of the fractional Brownian motion Potential Analysis 10 177-214
[3]  
Decreusefond L.(1997)On the prediction of fractional Brownian motion J. Appl. Probab. 33 400-410
[4]  
Üstünel A. S.(1998)Linear filtering with fractional Brownian motion Stoch. Anal. Appl. 16 907-914
[5]  
Gripenberg G.(1998)Nonlinear filtering with fractional Brownian motion Inf. Trans. Prob. 34 65-76
[6]  
Norros I.(1998)Filtering and parameter estimation in a simple linear model driven by a fractional Brownian motion Stat. Probab. Lett. 38 263-274
[7]  
Kleptsyna M. L.(1998)Une approche de type Girsanov pour le filtrage dans un syst`eme lin´eaire simple avec bruit brownien fractionnaire C.R. Acad. Sci. Paris t326 997-1002
[8]  
Kloeden P. E.(1999)An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions Bernoulli 5 571-587
[9]  
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[10]  
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