Home | Contents | Submissions, editors, etc. | Login | Search | EJP
 Electronic Communications in Probability > Vol. 14 (2009) > Paper 21 open journal systems 


Deviation inequalities and moderate deviations for estimators of parameters in an Ornstein-Uhlenbeck process with linear drift

Fuqing Gao, Wuhan University
Hui Jiang, Nanjing University of Aeronautics


Abstract
Some deviation inequalities and moderate deviation principles for the maximum likelihood estimators of parameters in an Ornstein-Uhlenbeck process with linear drift are established by the logarithmic Sobolev inequality and the exponential martingale method.


Full text: PDF

Pages: 210-223

Published on: May 24, 2009
Bibliography
  1. Bercu, B.; Rouault, A. Sharp large deviations for the Ornstein-Uhlenbeck process. Teor. Veroyatnost. i Primenen. 46 (2001), no. 1, 74--93; translation in Theory Probab. Appl. 46 (2002), no. 1, 1--19 MR1968706 (2004b:60075)
  2. Bobkov, S. G.; Götze, F. Exponential integrability and transportation cost related to logarithmic Sobolev inequalities. J. Funct. Anal. 163 (1999), no. 1, 1--28. MR1682772 (2000b:46059)
  3. Cattiaux, Patrick; Guillin, Arnaud. Deviation bounds for additive functionals of Markov processes. ESAIM Probab. Stat. 12 (2008), 12--29 (electronic). MR2367991 (2009b:60085)
  4. Dembo, A. Moderate deviations for martingales with bounded jumps. Electron. Comm. Probab. 1 (1996), no. 3, 11--17 (electronic). MR1386290 (97k:60077)
  5. Dembo, Amir; Zeitouni, Ofer. Large deviations techniques and applications.Second edition.Applications of Mathematics (New York), 38. Springer-Verlag, New York, 1998. xvi+396 pp. ISBN: 0-387-98406-2 MR1619036 (99d:60030)
  6. Deuschel, Jean-Dominique; Stroock, Daniel W. Large deviations.Pure and Applied Mathematics, 137. Academic Press, Inc., Boston, MA, 1989. xiv+307 pp. ISBN: 0-12-213150-9 MR0997938 (90h:60026)
  7. Djellout, H.; Guillin, A.; Wu, L. Transportation cost-information inequalities and applications to random dynamical systems and diffusions. Ann. Probab. 32 (2004), no. 3B, 2702--2732. MR2078555 (2005i:60031)
  8. Djellout, H.; Guillin, A.; Wu, L. Moderate deviations of empirical periodogram and non-linear functionals of moving average processes. Ann. Inst. H. Poincaré Probab. Statist. 42 (2006), no. 4, 393--416. MR2242954 (2007k:60076)
  9. Florens-Landais, Danielle; Pham, Huyên. Large deviations in estimation of an Ornstein-Uhlenbeck model. J. Appl. Probab. 36 (1999), no. 1, 60--77. MR1699608 (2000c:62141)
  10. Gourcy, Mathieu; Wu, Liming. Logarithmic Sobolev inequalities of diffusions for the $Lsp 2$ metric. Potential Anal. 25 (2006), no. 1, 77--102. MR2238937 (2008h:60214)
  11. Guillin, A.; Liptser, R. Examples of moderate deviation principle for diffusion processes. Discrete Contin. Dyn. Syst. Ser. B 6 (2006), no. 4, 803--828 (electronic). MR2223909 (2008a:60060)
  12. Ledoux, Michel. Concentration of measure and logarithmic Sobolev inequalities. Séminaire de Probabilités, XXXIII, 120--216, Lecture Notes in Math., 1709, Springer, Berlin, 1999. MR1767995 (2002j:60002)
  13. Ledoux, Michel. The concentration of measure phenomenon.Mathematical Surveys and Monographs, 89. American Mathematical Society, Providence, RI, 2001. x+181 pp. ISBN: 0-8218-2864-9 MR1849347 (2003k:28019)
  14. Lezaud, Pascal. Chernoff and Berry-Esséen inequalities for Markov processes. ESAIM Probab. Statist. 5 (2001), 183--201 (electronic). MR1875670 (2003e:60168)
  15. Kutoyants, Yury A. Statistical inference for ergodic diffusion processes.Springer Series in Statistics. Springer-Verlag London, Ltd., London, 2004. xiv+481 pp. ISBN: 1-85233-759-1 MR2144185 (2006b:62005)
  16. Prakasa Rao, B. L. S. Statistical Inference for Diffusion Type Processes. Oxford University Presss, New York,1999.
  17. Revuz, Daniel; Yor, Marc. Continuous martingales and Brownian motion.Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 293. Springer-Verlag, Berlin, 1991. x+533 pp. ISBN: 3-540-52167-4 MR1083357 (92d:60053)
  18. Wu, Liming. A deviation inequality for non-reversible Markov processes. Ann. Inst. H. Poincaré Probab. Statist. 36 (2000), no. 4, 435--445. MR1785390 (2001g:60061)













Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | EJP

Electronic Communications in Probability. ISSN: 1083-589X