[KSCI] Korea Science Citation Index Service

BERRY-ESSEEN BOUND FOR MLE FOR LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION

RAO B.L.S. PRAKASA (Department of Mathematics and Statistics, University of Hyderabad)

Publication Information

Journal of the Korean Statistical Society / v.34, no.4, 2005 , pp. 281-295 More about this Journal

Abstract

We investigate the rate of convergence of the distribution of the maximum likelihood estimator (MLE) of an unknown parameter in the drift coefficient of a stochastic process described by a linear stochastic differential equation driven by a fractional Brownian motion (fBm). As a special case, we obtain the rate of convergence for the case of the fractional Ornstein- Uhlenbeck type process studied recently by Kleptsyna and Le Breton (2002).

Keywords

Linear stochastic differential equations; fractional Ornstein- Uhlenbeck type process; fractional Brownian motion; Maximum likelihood estimation; Berry-Esseen bound;

Citations & Related Records

Reference

1	FELLER, W. (1968). An Introduction to Probability Theory and its Applications, Wiley, New York
2	KLEPTSYNA, M.L. AND LE BRETON, A. (2002). 'Statistical analysis of the fractional Ornstein-Uhlenbeck type process', Statistical Inference for Stochastic Processes, 5, 229-248 DOI ScienceOn
3	WATSON, G.N. (1995). A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge
4	MICHEL, R. AND PFANZAGL, J. (1971). 'The accuracy of the normal approximation for minimum contrast estimate', Z. Wahr. verw Gebeite, 18, 73-84 DOI
5	PRAKASA RAO, B.L.S. (1987). Asymptotic Theory of Statistical Inference, Wiley, New York
6	LE BRETON, A. (1998). 'Filtering and parameter estimation in a simple linear model driven by a fractional Brownian motion', Statistical Probability Letters, 38, 263-274 DOI ScienceOn
7	NORROS, I., VALKEILA, E., AND VIRTAMO, J. (1999). 'An elementary approach to a Girsanov type formula and other analytical results on fractional Brownian motion', Bernoulli, 5, 571-587 DOI ScienceOn
8	HALL, P. AND HEYDE, C.C. (1980). Martingale Limit Theory and its Applications, Academic Press, New York
9	SAMKO, S.G., KILBAS, A.A., AND MARICHEV, O.I. (1993). Fractional Integrals and derivatives, Gordon and Breach Science, Yverdon
10	PRAKASA RAO, B.L.S. (1999). Statistical Inference for Diffusion Type Processes, Arnold, London and Oxford University Press, New York
11	PRAKASA RAO, B.L.S. (2003). 'Parametric estimation for linear stochastic differential equations driven by fractional Brownian motion', Random Operators and Stochastic Equations, 11, 229-242 DOI
12	ALOS, E., MAZET, O., AND NUALART, D. (2001). 'Stochastic calculus with respect to gaussian processes', Annals of Probability, 29, 766-801 DOI ScienceOn
13	BOSE, A. (1986). 'Berry-Esseen bound for the maximum likelihood estimator in the Ornstein-Uhlenbeck process', Sankhya Ser.A, 48, 181-187
14	KLEPTSYNA, M.L. AND LE BRETON, A. AND ROUBAUD, M.-C. (2000). 'Parameter estimation and optimal filtering for fractional type stochastic systems', Statistical Inference for Stochastic Processes. 3. 173-182 DOI ScienceOn
15	IKEDA, N. AND WATANABE, S. (1981). Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam