Related papers: Parameter estimation for an Ornstein-Uhlenbeck Pro…
This article establishes cutoff thermalization (also known as the cutoff phenomenon) for a class of generalized Ornstein-Uhlenbeck systems $(X^\varepsilon_t(x))_{t\geqslant 0}$ with $\varepsilon$-small additive L\'evy noise and initial…
In this work, we provide the first strong convergence result of numerical approximation of a general second order semilinear stochastic fractional order evolution equation involving a Caputo derivative in time of order $\alpha\in(\frac 34,…
Let $u = \{u(t, x); (t,x)\in \mathbb R_+\times \mathbb R\}$ be the solution to a linear stochastic heat equation driven by a Gaussian noise, which is a Brownian motion in time and a fractional Brownian motion in space with Hurst parameter…
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…
The Ornstein-Uhlenbeck process may be used to generate a noise signal with a finite correlation time. If a one-dimensional stochastic process is driven by such a noise source, it may be analysed by solving a Fokker-Planck equation in two…
We consider the problem of frequency estimation of the periodic signal multiplied by a stationary Gaussian process (Ornstein-Uhlenbeck) and observed in the presence of the white Gaussian noise. We show the consistency and asymptotic…
The paper considers the problem of estimating a $p\geq2$\ dimensional mean vector of a multivariate conditionally normal distribution under quadratic loss. The problem of this type arises when estimating the parameters in a continuous time…
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…
A scalar Langevin-type process $X(t)$ that is driven by Ornstein-Uhlenbeck noise $\eta(t)$ is non-Markovian. However, the joint dynamics of $X$ and $\eta$ is described by a Markov process in two dimensions. But even though there exists a…
We develop the generalized method of moments (GMM) estimation for the parameters of the finitely mixed multi-mixed fractional Ornstein--Uhlenbeck (mmfOU) processes, and analyze the consistency and asymptotic normality of this estimator. We…
We study the problem of parameter estimation for the homogenization limit of multiscale systems involving fractional dynamics. In the case of stochastic multiscale systems driven by Brownian motion, it has been shown that in order for the…
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 investigate the concept of cylindrical Wiener process subordinated to a strictly $\alpha$-stable L\'evy process, with $\alpha\in\left(0,1\right)$, in an infinite dimensional, separable Hilbert space, and consider the related stochastic…
We consider the Graph Ornstein-Uhlenbeck (GrOU) process observed on a non-uniform discrete time grid and introduce discretised maximum likelihood estimators with parameters specific to the whole graph or specific to each component, or node.…
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|…
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…
This paper deals with the consistency and a rate of convergence for a Nadaraya-Watson estimator of the drift function of a stochastic differential equation driven by an additive fractional noise. The results of this paper are obtained via…
In this paper, we investigate the consistency and asymptotic efficiency of an estimator of the drift matrix, $F$, of Ornstein-Uhlenbeck processes that are not necessarily stable. We consider all the cases. (1) The eigenvalues of $F$ are in…
In this study, we generalize a problem of sampling a scalar Gauss Markov Process, namely, the Ornstein-Uhlenbeck (OU) process, where the samples are sent to a remote estimator and the estimator makes a causal estimate of the observed…
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…