Cramér-type moderate deviations for statistics in the non-stationary Ornstein–Uhlenbeck process

References

• E. Azmoodeh and J. Morlanes, Drift parameter estimation for fractional Ornstein-Uhlenbeck process of the second kind, Statistics 49 (2015), pp. 1–18. doi: 10.1080/02331888.2013.863888
   Web of Science ®Google Scholar
• B. Bercu, On large deviations in the Gaussian autoregressive process: Stable, unstable and explosive cases, Bernoulli 7 (2001), pp. 299–316. doi: 10.2307/3318740
   Web of Science ®Google Scholar
• B. Bercu and A. Rouault, Sharp large deviations for the Ornstein-Uhlenbeck process, Theor. Probab. Appl. 46 (2002), pp. 1–19. doi: 10.1137/S0040585X97978737
   Web of Science ®Google Scholar
• B. Bercu and A. Richou, Large deviations for the Ornstein-Uhlenbeck process with shift, Adv. Appl. Probab. 47 (2015), pp. 880–901. doi: 10.1239/aap/1444308886
   Web of Science ®Google Scholar
• B. Bercu and A. Richou, Large deviations for the Ornstein-Uhlenbeck process without tears, Stat. Probab. Lett. 123 (2017), pp. 45–55. doi: 10.1016/j.spl.2016.11.030
   Web of Science ®Google Scholar
• B. Bercu, L. Coutin, and N. Savy, Sharp large deviations for the non-stationary Ornstein-Uhlenbeck process, Stoch. Process. Appl. 122 (2012), pp. 3393–3424. doi: 10.1016/j.spa.2012.06.006
   Web of Science ®Google Scholar
• A.N. Borodin and P. Salminen, Handbook of Brownian Motion-facts and Formulae, Birkhäuser, Basel, 2015.
   Google Scholar
• Y. Chen, Y.Z. Hu, and Z. Wang, Parameter estimation of complex fractional Ornstein-Uhlenbeck processes with fractional noise, ALEA 14 (2017), pp. 613–629.
   Google Scholar
• H.M. Dietz and Yu.A. Kutoyants, Parameter estimation for some non-recurrent solutions of SDE, Statist. Decisions 21 (2003), pp. 29–45. doi: 10.1524/stnd.21.1.29.20321
   Google Scholar
• B. El Onsy, K. Es-Sebaiy, and F. Viens, Parameter estimation for a partially observed Ornstein-Uhlenbeck process with long-memory noise, Stochastics 89 (2017), pp. 431–468. doi: 10.1080/17442508.2016.1248967
   Web of Science ®Google Scholar
• B. El Onsy, K. Es-Sebaiy, and D. Ndiaye, Parameter estimation for discretely observed non-ergodic fractional Ornstein-Uhlenbeck processes of the second kind, Braz. J. Probab. Stat. 32 (2018), pp. 545–558. doi: 10.1214/17-BJPS353
   Web of Science ®Google Scholar
• P.D. Feigin, Some comments concerning a curious singularity, J. Appl. Probab. 16 (1979), pp. 440–444. doi: 10.2307/3212913
   Web of Science ®Google Scholar
• D. Florens-Landais and H. Pham, Large deviations in estimate of an Ornstein-Uhlenbeck model, J. Appl. Probab. 36 (1999), pp. 60–77. doi: 10.1239/jap/1032374229
   Web of Science ®Google Scholar
• F.Q. Gao and H. Jiang, Deviation inequalities and moderate deviations for estimators of parameters in an Ornstein-Uhlenbeck process with linear drift, Electron. Commun. Probab. 14 (2009), pp. 210–223. doi: 10.1214/ECP.v14-1466
   Web of Science ®Google Scholar
• F.Q. Gao and H. Jiang, Deviation inequalities for quadratic Wiener functionals and moderate deviations for parameter estimators, Sci. China Math. 60 (2017), pp. 1181–1196. doi: 10.1007/s11425-016-0017-6
   Web of Science ®Google Scholar
• F.Q. Gao, J. Xiong, and X.Q. Zhao, Moderate deviations and nonparametric inference for monotone functions, Ann. Stat. 46 (2018), pp. 1225–1254. doi: 10.1214/17-AOS1583
   Web of Science ®Google Scholar
• A. Guillin and R. Liptser, Examples of moderate deviation principles for diffusion processes, Discrete Cont. Dyn. Syst. B 6 (2006), pp. 77–102.
   Web of Science ®Google Scholar
• Y. Hu and D. Nualart, Parameter estimation for fractional Ornstein-Uhlenbeck processes, Stat. Probab. Lett. 80 (2010), pp. 1030–1038. doi: 10.1016/j.spl.2010.02.018
   Web of Science ®Google Scholar
• Y. Hu, D. Nualart, and H.J. Zhou, Parameter estimation for fractional Ornstein-Uhlenbeck processes of general Hurst parameter, Stat. Inference Stoch. Process 22 (2019), pp. 111–142. doi: 10.1007/s11203-017-9168-2
   Google Scholar
• H. Jiang, Berry-Esseen bounds and the law of iterated logarithm for estimators of parameters in an Ornstein-Uhlenbeck process with linear drift, J. Appl. Probab. 49 (2012), pp. 978–989. doi: 10.1239/jap/1354716652
   Web of Science ®Google Scholar
• H. Jiang and C. Xie, Asymptotic behaviours for the trajectory fitting estimator in Ornstein-Uhlenbeck process with linear drift, Stochastics 88 (2016), pp. 336–352. doi: 10.1080/17442508.2015.1066378
   Web of Science ®Google Scholar
• H. Jiang, J.F. Liu, and S.C. Wang, Self-normalized asymptotic properties for the parameter estimation in fractional Ornstein-Uhlenbeck process, Stoch. Dyn. 3 (2019), 1950018. doi: 10.1142/S0219493719500187
   Google Scholar
• C. Lee and J. Song, On drift parameter estimation for reflected fractional Ornstein-Uhlenbeck processes, Stochastics 88 (2016), pp. 751–778. doi: 10.1080/17442508.2016.1143472
   Web of Science ®Google Scholar
• P. Major, Tail behavior of multiple integrals and U-statistics, Probab. Surveys 2 (2005), pp. 448–505. doi: 10.1214/154957805100000186
   Google Scholar
• P. Major, On a multivariate version of Bernsteins inequality, Electron. J. Probab. 12 (2007), pp. 966–988. doi: 10.1214/EJP.v12-430
   Web of Science ®Google Scholar
• D. Nualart, The Malliavin Calculus and Related Topics, Springer-Verlag, New York, 2006.
   Google Scholar
• Y. Shimizu, Local asymptotic mixed normality for discretely observed non-recurrent Ornstein-Uhlenbeck processes, Ann. Inst. Stat. Math. 64 (2012), pp. 193–211. doi: 10.1007/s10463-010-0307-4
   Web of Science ®Google Scholar
• J. Worms, Large and moderate deviations upper bounds for the Gaussian autoregressive process, Sat. Probab. Lett. 51 (2001), pp. 235–243. doi: 10.1016/S0167-7152(00)00134-6
   Web of Science ®Google Scholar
• Q.P. Zang and L.X. Zhang, A general lower bound of parameter estimation for reflected Ornstein-Uhlenbeck processes, J. Appl. Probab. 53 (2016), pp. 22–32. doi: 10.1017/jpr.2015.5
   Web of Science ®Google Scholar
• Q.P. Zang and L.X. Zhang, Asymptotic behaviour of the trajectory fitting estimator for reflected Ornstein-Uhlenbeck processes, J. Theor. Probab. 32 (2019), pp. 183–201. doi: 10.1007/s10959-017-0796-7
   Web of Science ®Google Scholar