Related papers: Statistical Estimations for Non-Ergodic Vasicek Mo…

We study the problem of parameter estimation for a non-ergodic Gaussian Vasicek-type model defined as $dX_t=(\mu+\theta X_t)dt+dG_t,\ t\geq0$ with unknown parameters $\theta>0$ and $\mu\in\mathbb{R}$, where $G$ is a Gaussian process. We…

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…

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…

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…

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,\,…

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…

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…

The asymptotic analysis of covariance parameter estimation of Gaussian processes has been subject to intensive investigation. However, this asymptotic analysis is very scarce for non-Gaussian processes. In this paper, we study a class of…

The Berry-Ess\'{e}en upper bounds of moment estimators and least squares estimators of the mean and drift coefficients in Vasicek models driven by general Gaussian processes are studied. When studying the parameter estimation problem of…

We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…

We study the parameter estimation problem of Vasicek Model driven by sub-fractional Brownian processes from discrete observations, and let {S_t^H,t>=0} denote a sub-fractional Brownian motion whose Hurst parameter 1/2<H<1 . The studies are…

We study rates of convergence in central limit theorems for the partial sum of squares of general Gaussian sequences, using tools from analysis on Wiener space. No assumption of stationarity, asymptotically or otherwise, is made. The main…

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…

Gaussian process models typically contain finite dimensional parameters in the covariance function that need to be estimated from the data. We study the Bayesian fixed-domain asymptotics for the covariance parameters in a universal kriging…

This paper developed an inference problem for Vasicek model driven by a general Gaussian process. We construct a least squares estimator and a moment estimator for the drift parameters of the Vasicek model, and we prove the consistency and…

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…

We simultaneously estimate the four parameters of a subcritical Heston process. We do not restrict ourself to the case where the stochastic volatility process never reaches zero. In order to avoid the use of unmanageable stopping times and…

Consider a periodic, mean-reverting Ornstein-Uhlenbeck process $X=\{X_t,t\geq0\}$ of the form $d X_{t}=\left(L(t)+\alpha X_{t}\right) d t+ dB^H_{t}, \quad t \geq 0$, where $L(t)=\sum_{i=1}^{p}\mu_i\phi_i (t)$ is a periodic parametric…

The aim of this paper is twofold. First, it offers a novel formula to calculate the inner product of the bounded variation function in the Hilbert space $\mathcal{H}$ associated with the fractional Brownian motion with Hurst parameter $H\in…

Gaussian Process regression is a kernel method successfully adopted in many real-life applications. Recently, there is a growing interest on extending this method to non-Euclidean input spaces, like the one considered in this paper,…