Related papers: Drift estimation for a partially observed mixed fr…
This paper addresses the problem of estimating drift parameter of the Ornstein - Uhlenbeck type process, driven by the sum of independent standard and fractional Brownian motions. The maximum likelihood estimator is shown to be consistent…
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…
We consider Langevin equation involving fractional Brownian motion with Hurst index $H\in(0,\frac12)$. Its solution is the fractional Ornstein-Uhlenbeck process and with unknown drift parameter $\theta$. We construct the estimator that is…
In this paper, we consider the statistical inference of the drift parameter $\theta$ of non-ergodic Ornstein-Uhlenbeck~(O-U) process driven by a general Gaussian process $(G_t)_{t\ge 0}$. When $H \in (0, \frac 12) \cup (\frac 12,1) $ the…
We consider a stochastic differential equation involving standard and fractional Brownian motion with unknown drift parameter to be estimated. We investigate the standard maximum likelihood estimate of the drift parameter, two non-standard…
We consider a reflected Ornstein-Uhlenbeck process $X$ driven by a fractional Brownian motion with Hurst parameter $H\in (0, \frac12) \cup (\frac12, 1)$. Our goal is to estimate an unknown drift parameter $\alpha\in (-\infty,\infty)$ on the…
Fractional Ornstein-Uhlenbeck process of the second kind $(\text{fOU}_{2})$ is solution of the Langevin equation $\mathrm{d}X_t = -\theta X_t\,\mathrm{d}t+\mathrm{d}Y_t^{(1)}, \ \theta >0$ with driving noise $ Y_t^{(1)} := \int^t_0 e^{-s}…
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,…
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…
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…
We investigate large deviation properties of the maximum likelihood drift parameter estimator for Ornstein--Uhlenbeck process driven by mixed fractional Brownian motion.
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…
\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…
In this paper, we 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 $ R(t,\,…
We construct a least squares estimator for the drift parameters of a fractional Ornstein Uhlenbeck process with periodic mean function and long range dependence. For this estimator we prove consistency and asymptotic normality. In contrast…
Fractional Ornstein-Uhlenbeck process of the second kind $(\text{fOU}_{2})$ is solution of the Langevin equation $\mathrm{d}X_t = -\theta X_t\,\mathrm{d}t+\mathrm{d}Y_t^{(1)}, \ \theta >0$ with Gaussian driving noise $ Y_t^{(1)} := \int^t_0…
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…
In this paper, we investigate the parameter estimation for threshold Ornstein$\mathit{-}$Uhlenbeck processes. Least squares method is used to obtain continuous-type and discrete-type estimators for the drift parameters based on continuous…
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…
Consider an estimation of the Hurst parameter $H\in(0,1)$ and the volatility parameter $\sigma>0$ for a fractional Brownian motion with a drift term under high-frequency observations with a finite time interval. In the present paper, we…