Related papers: Parameter estimation for fractional Ornstein-Uhlen…
We consider the parameter estimation problem for the non-ergodic fractional Ornstein-Uhlenbeck process defined as $dX_t=\theta X_tdt+dB_t,\ t\geq0$, with a parameter $\theta>0$, where $B$ is a fractional Brownian motion of Hurst index…
This paper provides several statistical estimators for the drift and volatility parameters of an Ornstein-Uhlenbeck process driven by fractional Brownian motion, whose observations can be made either continuously or at discrete time…
We will study the least square estimator $\hat{\theta}_{T,S}$ for the drift parameter $\theta$ of the fractional Ornstein-Uhlenbeck sheet which is defined as the solution of the Langevin equation X_{t,s}= -\theta \int^{t}_{0} \int^{s}_{0}…
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}…
Let the Ornstein-Uhlenbeck process $(X_t)_{t\ge0}$ driven by a fractional Brownian motion $B^{H }$, described by $dX_t = -\theta X_t dt + \sigma dB_t^{H }$ be observed at discrete time instants $t_k=kh$, $k=0, 1, 2, \cdots, 2n+2 $. We…
Let $\theta>0$. We consider a one-dimensional fractional Ornstein-Uhlenbeck process defined as $dX_t= -\theta\ X_t dt+dB_t,\quad t\geq0,$ where $B$ is a fractional Brownian motion of Hurst parameter $H\in(1/2,1)$. We are interested in the…
Let $B^{a,b}:=\{B_t^{a,b},t\geq0\}$ be a weighted fractional Brownian motion of parameters $a>-1$, $|b|<1$, $|b|<a+1$. We consider a least square-type method to estimate the drift parameter $\theta>0$ of the weighted fractional…
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…
The statistical analysis for equations driven by fractional Gaussian process (fGp) is relatively recent. The development of stochastic calculus with respect to the fGp allowed to study such models. In the present paper we consider the drift…
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…
For an Ornstein-Uhlenbeck process driven by a fractional Brownian motion with Hurst parameter 0<H<1/2, one shows the Berry-Ess\'een bound of the least squares estimator of the drift parameter. Thus, a problem left in the previous paper…
\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…
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…
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…
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…
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…
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…
Starting from the notion of multivariate fractional Brownian Motion introduced in [F. Lavancier, A. Philippe, and D. Surgailis. Covariance function of vector self-similar processes. Statistics & Probability Letters, 2009] we define a…
It is considered Ornstein-Uhlenbeck process $ x_t = x_0 e^{-\theta t} + \mu (1-e^{-\theta t}) + \sigma \int_0^t e^{-\theta (t-s)} dW_s$, where $x_0 \in R$, $\theta>0$, $ \mu \in R$ and $\sigma > 0$ are parameters. By use values $(z_k)_{k…
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…