Parametric estimation for linear system of stochastic differential equations driven by fractional Brownian motions with different Hurst indices

Rao, B. L. S.

doi:10.1090/S0094-9000-09-00788-1

Parametric estimation for linear system of stochastic differential equations driven by fractional Brownian motions with different Hurst indices

Author: B. L. S. Prakasa Rao
Journal: Theor. Probability and Math. Statist. 79 (2009), 143-151
MSC (2000): Primary 62M09; Secondary 60G18
DOI: https://doi.org/10.1090/S0094-9000-09-00788-1
Published electronically: December 30, 2009
MathSciNet review: 2494544
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the problem of maximum likelihood estimation of the common trend parameter for a linear system of stochastic differential equations driven by two independent fractional Brownian motions possibly with different Hurst indices. Asymptotic properties of the maximum likelihood estimator are discussed.

References

M. L. Kleptsyna and A. Le Breton, Statistical analysis of the fractional Ornstein-Uhlenbeck type process, Stat. Inference Stoch. Process. 5 (2002), no. 3, 229–248. MR 1943832, DOI https://doi.org/10.1023/A%3A1021220818545
R. Sh. Liptser, A strong law of large numbers for local martingales, Stochastics 3 (1980), no. 3, 217–228. MR 573205, DOI https://doi.org/10.1080/17442508008833146

Y. Mishura and N. Rudomino-Dusyatska, Consistency of Drift Parameter Estimates in Fractional Brownian Diffusion Models, Research paper No. 04-2004, Acturial Education and Reference Centre of the Ukrainian Acturial Society, Lviv, Ukraine, 2004.

Ilkka Norros, Esko Valkeila, and Jorma Virtamo, An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions, Bernoulli 5 (1999), no. 4, 571–587. MR 1704556, DOI https://doi.org/10.2307/3318691

David Nualart and Aurel Răşcanu, Differential equations driven by fractional Brownian motion, Collect. Math. 53 (2002), no. 1, 55–81. MR 1893308

B. L. S. Prakasa Rao, Statistical inference for diffusion type processes, Kendall’s Library of Statistics, vol. 8, Edward Arnold, London; Oxford University Press, New York, 1999. MR 1717690

B. L. S. Prakasa Rao, Semimartingales and their statistical inference, Monographs on Statistics and Applied Probability, vol. 83, Chapman & Hall/CRC, Boca Raton, FL, 1999. MR 1689166

B. L. S. Prakasa Rao, Parametric estimation for linear stochastic differential equations driven by fractional Brownian motion, Random Oper. Stochastic Equations 11 (2003), no. 3, 229–242. MR 2009183, DOI https://doi.org/10.1163/156939703771378581

B. L. S. Prakasa Rao, Berry-Esseen bound for MLE for linear stochastic differential equations driven by fractional Brownian motion, J. Korean Statist. Soc. 34 (2005), no. 4, 281–295. MR 2233242

B. L. S. Prakasa Rao, Instrumental variable estimation for linear stochastic differential equations driven by fractional Brownian motion, Stoch. Anal. Appl. 25 (2007), no. 6, 1203–1215. MR 2367310, DOI https://doi.org/10.1080/07362990701567306

Michael Sørensen, Likelihood methods for diffusions with jumps, Statistical inference in stochastic processes, Probab. Pure Appl., vol. 6, Dekker, New York, 1991, pp. 67–105. MR 1138259

M. Zähle, Integration with respect to fractal functions and stochastic calculus. I, Probab. Theory Related Fields 111 (1998), no. 3, 333–374. MR 1640795, DOI https://doi.org/10.1007/s004400050171