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We investigate large deviation properties of the maximum likelihood drift parameter estimator for Ornstein--Uhlenbeck process driven by mixed fractional Brownian motion.

Probability · Mathematics 2016-07-14 Dmytro Marushkevych

We construct the least-square estimator for the unknown drift parameter in the multifractional Ornstein-Uhlenbeck model and establish its strong consistency in the non-ergodic case. The proofs are based on the asymptotic bounds with…

Probability · Mathematics 2016-02-19 Marco Dozzi , Yuriy Kozachenko , Yuliya Mishura , Kostiantyn Ralchenko

We consider the problem of efficient estimation of the drift parameter of an Ornstein-Uhlenbeck type process driven by a L\'{e}vy process when high-frequency observations are given. The estimator is constructed from the time-continuous…

Statistics Theory · Mathematics 2014-03-13 Hilmar Mai

For an Ornstein-Uhlenbeck process driven by fractional Brownian motion with Hurst index $H\in [\frac12,\frac34]$, we show the Berry-Ess\'een bound of the least squares estimator of the drift parameter. We use an approach based on Malliavin…

Probability · Mathematics 2019-08-16 Yong Chen , Nenghui Kuang , Ying Li

In this paper, we will first give the numerical simulation of the sub-fractional Brownian motion through the relation of fractional Brownian motion instead of its representation of random walk. In order to verify the rationality of this…

Probability · Mathematics 2021-01-11 Chunhao Cai , Qinghua Wang , Weilin Xiao

We obtain a Berry-Esseen type bound for the distribution of the maximum likelihood estimator of the drift parameter for fractional Ornstein-uhlenbeck type process driven by sub-fractional Brownian motion.

Probability · Mathematics 2019-01-21 B. L. S. Prakasa Rao

In Chen and Zhou 2021, they consider an inference problem for an Ornstein-Uhlenbeck process driven by a general one-dimensional centered Gaussian process $(G_t)_{t\ge 0}$. The second order mixed partial derivative of the covariance function…

Statistics Theory · Mathematics 2021-12-30 Yong Chen , Xiangmeng Gu , Ying Li

This paper is devoted to parameter estimation of the mixed fractional Ornstein-Uhlenbeck process with a drift. Large sample asymptotical properties of the Maximum Likelihood Estimator is deduced using the Laplace transform computations or…

Statistics Theory · Mathematics 2021-01-19 Chunhao Cai , Min Zhang

The paper is devoted to three-parametric self-similar Gaussian Volterra processes that generalize fractional Brownian motion. We study the asymptotic growth of such processes and the properties of long- and short-range dependence. Then we…

Statistics Theory · Mathematics 2023-02-08 Yuliya Mishura , Kostiantyn Ralchenko , Sergiy Shklyar

\noindent \textbf{Abstract}: We consider the parameter estimation problem for the Ornstein-Uhlenbeck process $X$ driven by a fractional Ornstein-Uhlenbeck process $V$, i.e. the pair of processes defined by the non-Markovian continuous-time…

Probability · Mathematics 2016-10-14 Brahim El Onsy , Khalifa Es-Sebaiy , Frederi G. Viens

In the paper we consider the problem of estimating parameters entering the drift of a fractional Ornstein-Uhlenbeck type process in the non-ergodic case, when the underlying stochastic integral is of Young type. We consider the sampling…

Probability · Mathematics 2019-03-20 Radomyra Shevchenko , Jeannette H. C. Woerner

We consider estimation of the drift parameter $\vartheta>0$ in a \emph{partially observed} Ornstein--Uhlenbeck type model driven by a mixed fractional Brownian noise. Our framework extends the partially observed model of…

Statistics Theory · Mathematics 2026-01-12 Chunhao Cai

In the present paper we consider the Ornstein-Uhlenbeck process of the second kind defined as solution to the equation $dX_{t} = -\alpha X_{t}dt+dY_{t}^{(1)}, \ \ X_{0}=0$, where $Y_{t}^{(1)}:=\int_{0}^{t}e^{-s}dB^H_{a_{s}}$ with…

Probability · Mathematics 2020-05-19 Maoudo Faramba Balde , Rachid Belfadli , Khalifa Es-Sebaiy

We obtain strong consistency and asymptotic normality of a least squares estimator of the drift coefficient for complex-valued Ornstein-Uhlenbeck processes disturbed by fractional noise, extending the result of Y. Hu and D. Nualart,…

Probability · Mathematics 2017-01-27 Yong Chen , Yaozhong Hu , Zhi Wang

We investigate the problem of estimating the drift parameter of a high-dimensional L\'evy-driven Ornstein--Uhlenbeck process under sparsity constraints. It is shown that both Lasso and Slope estimators achieve the minimax optimal rate of…

Statistics Theory · Mathematics 2022-05-17 Niklas Dexheimer , Claudia Strauch

We consider the class of all stationary Gaussian process with explicit parametric spectral density. Under some conditions on the autocovariance function, we defined a GMM estimator that satisfies consistency and asymptotic normality, using…

Statistics Theory · Mathematics 2017-01-18 Luis A. Barboza , Frederi G. Viens

We study the strong consistency and asymptotic normality of a least squares estimator of the drift coefficient in complex-valued Ornstein-Uhlenbeck processes driven by fractional Brownian motion, extending the results of Chen, Hu, Wang…

Probability · Mathematics 2024-06-27 Fares Alazemi , Abdulaziz Alsenafi , Yong Chen , Hongjuan Zhou

This paper deals with the Local Asymptotical normality for the joint drift parameter and Hurst parameter $H>3/4$ in the mixed fractional Ornstein-Uhlenbeck process. Different from the only estimation of the drift parameter when $H$ is…

Probability · Mathematics 2025-10-21 Chunhao Cai , Cong Zhang

We study the problem of parametric estimation for continuously observed stochastic processes driven by additive small fractional Brownian motion with Hurst index 0<H<1/2 and 1/2<H<1. Under some assumptions on the drift coefficient, we…

Statistics Theory · Mathematics 2022-01-04 Shohei Nakajima , Yasutaka Shimizu

Assuming that a threshold Ornstein-Uhlenbeck process is observed at discrete time instants, we propose generalized moment estimators to estimate the parameters. Our theoretical basis is the celebrated ergodic theorem. To use this theorem we…

Statistics Theory · Mathematics 2020-11-24 Yaozhong Hu , Yuejuan Xi