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

Stochastics ◽  
2019 ◽  
Vol 92 (3) ◽  
pp. 478-496
Author(s):  
Hui Jiang ◽  
Ning Zhang
Keyword(s):  
Moderate Deviations ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process

Self-normalized asymptotic properties for the parameter estimation in fractional Ornstein–Uhlenbeck process

2019 ◽  
Vol 19 (03) ◽  
pp. 1950018 ◽  
Author(s):  
Hui Jiang ◽  
Junfeng Liu ◽  
Shaochen Wang
Keyword(s):  
Large Deviations ◽  
Asymptotic Properties ◽  
Moderate Deviations ◽  
Delta Method ◽  
Fourth Moment ◽  
Test Statistics ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Deviation Inequalities ◽  
Type Ii Errors

In this paper, we consider the self-normalized asymptotic properties of the parameter estimators in the fractional Ornstein–Uhlenbeck process. The deviation inequalities, Cramér-type moderate deviations and Berry–Esseen bounds are obtained. The main methods include the deviation inequalities and moderate deviations for multiple Wiener–Itô integrals [P. Major, Tail behavior of multiple integrals and U-statistics, Probab. Surv. 2 (2005) 448–505; On a multivariate version of Bernsteins inequality, Electron. J. Probab. 12 (2007) 966–988; M. Schulte and C. Thäle, Cumulants on Wiener chaos: Moderate deviations and the fourth moment theorem, J. Funct. Anal. 270 (2016) 2223–2248], as well as the Delta methods in large deviations [F. Q. Gao and X. Q. Zhao, Delta method in large deviations and moderate deviations for estimators, Ann. Statist. 39 (2011) 1211–1240]. For applications, we propose two test statistics which can be used to construct confidence intervals and rejection regions in the hypothesis testing for the drift coefficient. It is shown that the Type II errors tend to be zero exponential when using the proposed test statistics.

Cramér-type moderate deviations for the likelihood ratio process of Ornstein–Uhlenbeck process with shift

2020 ◽  
Vol 21 (02) ◽  
pp. 2150027
Author(s):  
Hui Jiang ◽  
Hui Liu
Keyword(s):  
Likelihood Ratio ◽  
Decay Rates ◽  
Moderate Deviations ◽  
Uhlenbeck Process ◽  
Testing Problem ◽  
Analysis Techniques ◽  
Log Likelihood ◽  
Ornstein Uhlenbeck Process ◽  
Deviation Inequalities ◽  
Error Probabilities

For the Ornstein–Uhlenbeck process in stationary and explosive cases, this paper studies Cramér-type moderate deviations for the log-likelihood ratio process. As an application, we give the negative regions of drift testing problem, and also obtain the decay rates of the error probabilities. The main methods of this paper consist of mod-[Formula: see text] convergence approach, deviation inequalities for multiple Wiener–Itô integrals and asymptotic analysis techniques.

scholarly journals Time-changed fractional Ornstein-Uhlenbeck process

2020 ◽  
Vol 23 (2) ◽  
pp. 450-483 ◽  
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Planck Equation ◽  
Uhlenbeck Process ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

Sign in / Sign up

Export Citation Format

Share Document