Large and moderate deviations in testing Ornstein-Uhlenbeck process with linear drift

doi:10.1007/s11464-016-0513-3

Front. Math. China

2016, Vol. 11

Issue (2) : 291-307 https://doi.org/10.1007/s11464-016-0513-3

RESEARCH ARTICLE

Large and moderate deviations in testing Ornstein-Uhlenbeck process with linear drift

Hui JIANG(

)

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Download: PDF(161 KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

This paper studies hypothesis testing in the Ornstein-Ulenbeck process with linear drift. With the help of large and moderate deviations for the log-likelihood ratio process, the decision regions and the corresponding decay rates of the error probabilities related to this testing problem are established.

Keywords Hypothesis testing large deviations log-likelihood ratio process moderate deviations Ornstein-Uhleneck (O-U) process

Corresponding Author(s): Hui JIANG

Issue Date: 18 April 2016

Cite this article:

Hui JIANG. Large and moderate deviations in testing Ornstein-Uhlenbeck process with linear drift[J]. Front. Math. China, 2016, 11(2): 291-307.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-016-0513-3
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I2/291

1	Bercu B, Richou A. Large deviations for the Ornstein-Uhlenbeck process with shift. Adv in Appl Probab, 2015, 47: 880–901 https://doi.org/10.1017/S0001867800048874
2	Bercu B, Rouault A. Sharp large deviations for the Ornstein-Uhlenbeck process. Theory Probab Appl, 2002, 46: 1–19 https://doi.org/10.1137/S0040585X97978737
3	Bishwal J P N. Large deviations in testing fractional Ornstein-Uhlenbeck models. Statist Probab Lett, 2008, 78: 953–962 https://doi.org/10.1016/j.spl.2007.09.055
4	Blahut R E. Hypothesis testing and information theory. IEEE Trans Inform Theory, 1984, 20: 405–415 https://doi.org/10.1109/TIT.1974.1055254
5	Chiyonobu T. Hypothesis testing for signal detection problem and large deviations. Nagoya Math J, 2003, 162: 187–203
6	Dembo A, Zeitouni D. Large Deviations Techniques and Applications. Berlin: Springer- Verlag, 1998 https://doi.org/10.1007/978-1-4612-5320-4
7	Demni N, Zani M. Large deviations for statistics of Jacobi process. Stochastic Process Appl, 2009, 119: 518–533 https://doi.org/10.1016/j.spa.2008.02.015
8	Florens-Landais D, Pham H. Large deviations in estimate of an Ornstein-Uhlenbeck model. J Appl Probab, 1999, 36: 60–77 https://doi.org/10.1239/jap/1032374229
9	Gao F Q, Jiang H. Deviation inequalities and moderate deviations for estimators of parameters in an Ornstein-Uhlenbeck process with linear drift. Electron Commun Probab, 2009, 14: 210–223 https://doi.org/10.1214/ECP.v14-1466
10	Gao F Q, Zhao S J. Moderate deviations and hypothesis testing for signal detection problem. Sci China Math, 2012, 55: 2273–2284 https://doi.org/10.1007/s11425-012-4514-8
11	Gepeev P V, Küchler U. On large deviations in testing Ornstein-Uhlenbeck-type models. Stat Inference Stoch Process, 2008, 11: 143–155 https://doi.org/10.1007/s11203-007-9012-1
12	Guillin A, Liptser R. Examples of moderate deviation principles for diffusion processes. Discrete Contin Dyn Syst Ser B, 2006, 6: 77–102
13	Jiang H, Zhao S J. Large and moderate deviations in testing time inhomogeneous diffusions. J Statist Plann Inference, 2011, 141: 3160–3169 https://doi.org/10.1016/j.jspi.2011.04.003
14	Kuang N H, Xie H T. Large and moderate deviations in testing Rayleigh diffusion model. Statist Papers, 2013, 54: 591–603 https://doi.org/10.1007/s00362-012-0450-5
15	Kutoyants Yu A. Statistical Inference for Ergodic Diffusion Process. Berlin: Springer, 2003
16	Zani M. Large deviations for squared radial Ornstein-Uhlenbeck processes. Stochastic Process Appl, 2002, 102: 25–42 https://doi.org/10.1016/S0304-4149(02)00156-4
17	Zhao S J. Hypothesis testing for fractional Ornstein-Uhlenbeck model. Acta Math Sci Ser A Chin Ed, 2011, 31: 1393–1402 (in Chinese)
18	Zhao S J, Gao F Q. Large deviations in testing Jacobi model. Statist Probab Lett, 2010, 80: 34–41 https://doi.org/10.1016/j.spl.2009.09.009

[1]	Xiequan FAN, Haijuan HU, Quansheng LIU. Uniform Cramér moderate deviations and Berry-Esseen bounds for a supercritical branching process in a random environment[J]. Front. Math. China, 2020, 15(5): 891-914.
[2]	Xiaocui MA, Fubao XI, Dezhi LIU. Moderate deviations for neutral functional stochastic differential equations driven by Levy noises[J]. Front. Math. China, 2020, 15(3): 529-554.
[3]	Fuqing GAO, Qiaojing LIU. Moderate deviations for estimators under exponentially stochastic differentiability conditions[J]. Front. Math. China, 2018, 13(1): 25-40.
[4]	Qi SUN, Mei ZHANG. Harmonic moments and large deviations for supercritical branching processes with immigration[J]. Front. Math. China, 2017, 12(5): 1201-1220.
[5]	Lei CHEN, Shaochen WANG. Asymptotic behavior for log-determinants of several non-Hermitian rand om matrices[J]. Front. Math. China, 2017, 12(4): 805-819.
[6]	Xinmei SHEN, Yuqing NIU, Hailan TIAN. Precise large deviations for sums of random vectors with dependent components of consistently varying tails[J]. Front. Math. China, 2017, 12(3): 711-732.
[7]	Kaiyong WANG, Yang YANG, Jinguan LIN. Precise large deviations for widely orthant dependent random variables with dominatedly varying tails[J]. Front Math Chin, 2012, 7(5): 919-932.
[8]	Jun FAN, Fuqing GAO. Deviation inequalities and moderate deviations for estimators of parameters in TAR models[J]. Front Math Chin, 2011, 6(6): 1067-1083.

Viewed

Full text

Abstract

Cited

Shared

Discussed