Parametric estimation for linear stochastic delay differential equations driven by fractional Brownian motion

Random Operators and Stochastic Equations

Volumn 16, Issue 1, 2008, Pages 27-38

  Prakasa Rao, B L S ^a  

^a UNIVERSITY OF HYDERABAD   (India)

Author keywords

Consistency; Fractional Brownian motion; Fractional ornstein uhlenbeck type process; Linear stochastic differential equation; Local asymptotic mixed normality; Local asymptotic normality; Maximum likelihood estimation; Time delay

Indexed keywords

EID: 78650697175     PISSN: 09266364     EISSN: 1569397X     Source Type: Journal    
DOI: 10.1515/ROSE.2008.003     Document Type: Article

References (17)

1. A. A. Gushchin and V. Kuchler, Asymptotic inference for a linear stochastic differential equation with time delay. Bernoulli 5 (1999), 1059-1098.
2. M. L. Kleptsyna and A. Le Breton, Statistical analysis of the fractional Ornstein-Uhlenbeck type process. Statist. Infer. for Stoch. Proc. 5 (2002), 229-248.
3. M. L. Kleptsyna, A. Le Breton and M.-C. Roubaud, Parameter estimation and optimal filtering for fractional type stochastic systems. Statist. Infer. for Stoch. Proc. 3 (2000), 173-182.
4. A. Le Breton, Filtering and parameter estimation in a simple linear model driven by a fractional Brownian motion. Statist. Probab. Lett. 38 (1998), 263-274.
5. S.-E. A. Mohammed and M. K. R. Scheutzow, Lyapunov exponents and stationary solutions for affine stochastic delay equations. Stochastics and Stochastic Rep. 29 (1990), 259-283.
6. I. Norros, E. Valkeila and J. Virtamo, An elementary approach to a Girsanov type formula and other analytical results on fractional Brownian motion. Bernoulli 5 (1999), 571-587.
7. B. L. S. Prakasa Rao, Asymptotic Theory of Statistical Inference. Wiley, New York, 1987.
8. B. L. S. Prakasa Rao, Statistical Inference for Diffusion Type Processes. Arnold, London and Oxford University Press, New York, 1999.
9. B. L. S. Prakasa Rao, Semimartingales and Their Statistical Inference. CRC Press, Boca Raton and Chapman and Hall, London, 1999.
10. B. L. S. Prakasa Rao, Parametric estimation for linear stochastic differential equations driven by fractional Brownian motion. Random Oper. and Stoch. Equ. 11 (2003), 229-242.
11. B. L. S. Prakasa Rao, Sequential estimation for fractional Ornstein-Uhlenbeck type process. Sequential Analysis 23 (2004), 33-44.
12. B. L. S. Prakasa Rao. Identification for linear stochastic systems driven by fractional Brownian motion. Stochastic Anal. Appl. 22 (2004), 1487-1509. (Pubitemid 39483484)
13. B. L. S. Prakasa Rao, Self-similar processes, fractional Brownian motion and statistical inference. In Festschrift for Herman Rubin (ed. A. Das Gupta), Lecture Notes and Monograph Series, Institute of Mathematical Statistics, U. S. A, Vol. 45 (2004), 98-125.
14. B. L. S. Prakasa Rao, Berry-Esseen bound for MLE for linear stochastic differential equations driven by fractional Brownian motion. Journal of Korean Statistical Society 34 (2005), 281-295.
15. B. L. S. Prakasa Rao, Sequential testing for simple hypotheses for processes driven by fractional Brownian motion. Sequential Analysis 24 (2005), 189-203.
16. S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives. Gordon and Breach Science, Yverdon, 1993.
17. M. Sorensen, Likelihood methods for diffusions with jumps. In Statistical Inference in Stochastic Processes (ed. N. U. Prabhu and I. V. Basawa), Marcel Dekker, New York, pp. 67-105, 1991.