Related papers: Parameter estimation for fractional Ornstein-Uhlen…
We study the estimation of the invariant density of additive fractional stochastic differential equations with Hurst parameter $H \in (0,1)$. We first focus on continuous observations and develop a kernel-based estimator achieving faster…
In this paper we investigate the existence and some useful properties of the L\'evy areas of Ornstein-Uhlenbeck processes associated to Hilbert-space-valued fractional Brownian-motions with Hurst parameter $H\in (1/3,1/2]$. We prove that…
We investigate the asymptotic properties of the minimum $L_1$-norm estimator of the drift parameter for fractional Ornstein-Uhlenbeck type process driven by a Hermite process.
We study the approximation of stochastic differential equations driven by a fractional Brownian motion with Hurst parameter $H>1/2$. For the mean-square error at a single point we derive the optimal rate of convergence that can be achieved…
We investigate the asymptotic properties of the minimum $L_1$-norm estimator of the drift parameter for fractional Ornstein-Uhlenbeck type process driven by a general Gaussian process.
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…
We refer by threshold Ornstein-Uhlenbeck to a continuous-time threshold autoregressive process. It follows the Ornstein-Uhlenbeck dynamics when above or below a fixed level, yet at this level (threshold) its coefficients can be…
We extend the theoretical results for any FOU(p) processes for the case in which the Hurst parameter is less than 1/2 and we show theoretically and by simulations that under some conditions on T and the sample size n it is possible to…
In this article, we develop a Bayesian approach to estimate parameters from time traces that originate from an overdamped Brownian particle in a harmonic potential, or Ornstein-Uhlenbeck process (OU). We show that least-square fitting the…
In this paper, we apply rough paths techniques to provide an approximation of the solution of stochastic functional differential equations driven by fractional Brownian motion with Hurst parameter $H>1/2$. Here, the involved stochastic…
We prove a functional limit theorem for vector-valued functionals of the fractional Ornstein-Uhlenbeck process, providing the foundation for the fluctuation theory of slow/fast systems driven by such a noise. Our main contribution is on the…
We study the problem of parameter estimation for reflected stochastic processes driven by a standard Brownian motion. The estimator is obtained using nonlinear least squares method based on discretely observed processes. Under some certain…
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…
Let $Z$ be a $H$-valued Ornstein--Uhlenbeck process, $b\colon[0,1]\times H \rightarrow H$ and $h\colon[0,1] \rightarrow H$ be a bounded, Borel measurable functions with $\|b\|_\infty \leq 1$ then $\mathbb E \exp \alpha \left|…
We study the statistical inference problem for a complex $\alpha$-fractional Brownian bridge process $Z$ defined by the stochastic differential equation \[ \mathrm{d}Z_t = -\alpha \frac{Z_t}{T - t} \mathrm{d}t + \mathrm{d}\zeta_t, \quad t…
In this paper, we construct consistent statistical estimators of the Hurst index, volatility coefficient, and drift parameter for Bessel processes driven by fractional Brownian motion with $H<1/2$. As an auxiliary result, we also prove the…
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.
We prove the transfer principle for fractional Ornstein-Uhlenbeck processes, i.e., we construct a Brownian motion that has the same filtration as the fractional Ornstein-Uhlenbeck process and then represent the fractional Ornstein-Uhlenbeck…
This paper considers the effect of least squares procedures for nearly unstable linear time series with strongly dependent innovations. Under a general framework and appropriate scaling, it is shown that ordinary least squares procedures…
The purpose of this paper is to establish the multivariate normal convergence for the average of certain Volterra processes constructed from a fractional Brownian motion with Hurst parameter H>1/2. Some applications to parameter estimation…