Identification for linear stochastic systems driven by fractional Brownian motion

Stochastic Analysis and Applications

Volumn 22, Issue 6, 2004, Pages 1487-1509

  Prakasa Rao, B L S ^a  

^a INDIAN STATISTICAL INSTITUTE   (India)

Author keywords

Asymptotic normality; Consistency; Fractional Brownian motion; Fractional Ornstein Uhlenbeck process; Identification; Linear stochastic systems; Method of sieves; Nonparametric estimation; Stochastic differential equations

Indexed keywords

EID: 8344227545     PISSN: 07362994     EISSN: None     Source Type: Journal    
DOI: 10.1081/SAP-200029489     Document Type: Article

References (11)

1. Kleptsyna, M.L.; Le Breton, A. Statistical analysis of the fractional Ornstein-Uhlenbeck type process. Statist. Inf. Stochast. Proces. 2002, 5, 229-248.
2. Kleptsyna, M.L.; Le Breton, A.; Roubaud, M.-C. Parameter estimation and optimal filtering for fractional type stochastic systems. Statist. Inf. Stochast. Proces. 2000, 3, 173-182.
3. Le Breton, A. Filtering and parameter estimation in a simple linear model driven by a fractional Brownian motion. Stat. Probab. Lett. 1998, 38, 263-274.
4. Norros, I.; Valkeila, E.; Viratmo, J. An elementary approach to a Girsanov type formula and other analytical results on fractional Brownian motion. Bernoulli 1999, 5, 571-587.
5. Pham, T. D.; Nguyen, H.T. Identification of nonstationary diffusion model by the method of sieves. SIAM J. Control Optimization 1982, 20, 603-611.
6. Prakasa Rao, B.L.S. Statistical Inference for Diffusion Type Processes; Arnold, London and Oxford University Press: New York, 1999a.
7. Prakasa Rao, B.L.S. Semimartingales and Their Statistical Inference; CRC Press, Boca Raton and Chapman and Hall: London, 1999b.
8. Prakasa Rao, B.L.S. Parametric estimation for linear stochastic differential equations driven by fractional Brownian motion. Random Ope. Stoch. Equ. 2003a, 11, 229-242.
9. Prakasa Rao, B.L.S. Berry-Esseen bound for MLE for linear stochastic differential equations driven by fractional Brownian motion. Preprint, Indian Statistical Institute, New Delh, 2003b.
10. Prakasa Rao, B.L.S. Sequential estimation for fractional Ornstein-Uhlenbeck type process. Sequential Analy. 2004, 23, 33-44.
11. Samko, S.G.; Kilbas, A.A.; Marichev, O.I. Fractional Integrals and Derivatives; Gordon and Breach Science, 1993.