Parameter estimation for fractional Ornstein–Uhlenbeck processes of general Hurst parameter

Y Hu, D Nualart, H Zhou - Statistical Inference for Stochastic Processes, 2019 - Springer
This paper studies the least squares estimator (LSE) for the drift parameter of an Ornstein–
Uhlenbeck process driven by fractional Brownian motion, whose observations can be made …

Parameter estimation for an Ornstein-Uhlenbeck process driven by a general Gaussian noise

Y Chen, H Zhou - Acta Mathematica Scientia, 2021 - Springer
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≥ 0. The second order …

Vector‐valued generalized Ornstein–Uhlenbeck processes: Properties and parameter estimation

M Voutilainen, L Viitasaari, P Ilmonen… - … Journal of Statistics, 2022 - Wiley Online Library
Abstract Generalizations of the Ornstein–Uhlenbeck process defined through Langevin
equations, such as fractional Ornstein–Uhlenbeck processes, have recently received a lot of …

Berry-Esseen bounds of second moment estimators for Gaussian processes observed at high frequency

S Douissi, K Es-Sebaiy, G Kerchev… - Electronic Journal of …, 2022 - projecteuclid.org
Abstract Let Z:={Z t, t≥ 0} be a stationary Gaussian process. We study two estimators of E [Z
0 2], namely f ˆ T (Z):= 1 T∫ 0 TZ t 2 dt, and f˜ n (Z):= 1 n∑ i= 1 n Z ti 2, where ti= i Δ n, i= 0 …

Least squares estimator of fractional Ornstein–Uhlenbeck processes with periodic mean

S Bajja, K Es-Sebaiy, L Viitasaari - Journal of the Korean Statistical Society, 2017 - Elsevier
We first study the drift parameter estimation of the fractional Ornstein–Uhlenbeck process
(fOU) with periodic mean for every 1 2< H< 1. More precisely, we extend the consistency …

Berry–Esséen bound for the parameter estimation of fractional Ornstein–Uhlenbeck processes

Y Chen, N Kuang, Y Li - Stochastics and Dynamics, 2020 - World Scientific
For an Ornstein–Uhlenbeck process driven by fractional Brownian motion with Hurst index
H∈[1 2, 3 4], we show the Berry–Esséen bound of the least squares estimator of the drift …

Berry-Esséen bound for the parameter estimation of fractional Ornstein-Uhlenbeck processes with the hurst parameter

Y Chen, Y Li - Communications in Statistics-Theory and Methods, 2021 - Taylor & Francis
Abstract For an Ornstein–Uhlenbeck process driven by a fractional Brownian motion with
Hurst parameter H∈(0, 1 2), one shows the Berry–Esséen bound of the least squares …

Stochastic analysis of Gaussian processes via Fredholm representation

T Sottinen, L Viitasaari - International journal of stochastic …, 2016 - Wiley Online Library
We show that every separable Gaussian process with integrable variance function admits a
Fredholm representation with respect to a Brownian motion. We extend the Fredholm …

Central limit theorems and minimum-contrast estimators for linear stochastic evolution equations

P Kříž, B Maslowski - Stochastics, 2019 - Taylor & Francis
Central limit theorems and asymptotic properties of the minimum-contrast estimators of the
drift parameter in linear stochastic evolution equations driven by fractional Brownian motion …

[HTML][HTML] Long-range dependent completely correlated mixed fractional Brownian motion

J Dufitinema, F Shokrollahi, T Sottinen… - Stochastic Processes and …, 2024 - Elsevier
In this paper we introduce the long-range dependent completely correlated mixed fractional
Brownian motion (ccmfBm). This is a process that is driven by a mixture of Brownian motion …