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

Theory of Probability and Mathematical Statistics

Volumn 79, Issue , 2009, Pages 143-151

  Prakasa Rao, B L S ^a  

^a UNIVERSITY OF HYDERABAD   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85009807726     PISSN: 00949000     EISSN: 15477363     Source Type: Journal    
DOI: 10.1090/S0094-9000-09-00788-1     Document Type: Article

References (12)

1. M. L. Kleptsyna and A. Le Breton, Statistical analysis of the fractional Ornstein–Uhlenbeck type process, Statist. Inf. Stochast. Proces. 5 (2002), 229–248. MR1943832 (2003i:62140)
2. R. Liptser, A strong law of large numbers for local martingales, Stochastics, 3 (1980), 217–228. MR573205 (83d:60057)
3. 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.
4. I. Norros, E. Valkeila, and J. Virtamo, An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motion, Bernoulli, 55 (1999), 571–587. MR1704556 (2000f:60053)
5. D. Nualart and A. Rascanu, Differential Equations Driven by Fractional Brownian Motion, Preprint, 2001. MR1893308 (2003f:60105)
6. B. L. S. Prakasa Rao, Statistical Inference for Diffusion Type Processes, Arnold, London, and Oxford University Press, New York, 1999a. MR1717690 (2000k:62149)
7. B. L. S. Prakasa Rao, Semimartingales and their Statistical Inference, CRC Press, Boca Raton and Chapman and Hall, London, 1999b. MR1689166 (2000h:62004)
8. B. L. S. Prakasa Rao, Parametric estimation for linear stochastic differential equations driven by fractional Brownian motion, Random Operators and Stochastic Equations, 11 (2003), 229–242. MR2009183 (2005a:62188)
9. 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. MR2233242 (2007m:62128)
10. B. L. S. Prakasa Rao, Instrumental variable estimation for linear stochastic differential equations driven by fractional Brownian motion, Stochastic Analysis and Applications 25 (2007), no. 6, 1203–1215. MR2367310 (2009b:62169)
11. M. Sorensen, Likelihood methods for diffusions with jumps, Statistical Inference in Stochastic Processes (N. U. Prabhu and I. V. Basawa, eds.), Marcel Dekker, New York, 1991, 67–105. MR1138259 (92k:62144)
12. M. Zähle, Integration with respect to fractional functions and stochastic calculus I, Prob. Theory Relat. Fields, 111 (1998), 333–374. MR1640795 (99j:60073)