Least squares estimator for non-ergodic Ornstein–Uhlenbeck processes driven by Gaussian processes
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 …
recent. The development of stochastic calculus with respect to the fGp allowed to study such …
[HTML][HTML] Optimal rates for parameter estimation of stationary Gaussian processes
K Es-Sebaiy, FG Viens - Stochastic Processes and their Applications, 2019 - Elsevier
We study rates of convergence in central limit theorems for partial sums of polynomial
functionals of general stationary and asymptotically stationary Gaussian sequences, using …
functionals of general stationary and asymptotically stationary Gaussian sequences, using …
Parameter estimation based on discrete observations of fractional Ornstein–Uhlenbeck process of the second kind
E Azmoodeh, L Viitasaari - Statistical Inference for Stochastic Processes, 2015 - Springer
Abstract Fractional Ornstein–Uhlenbeck process of the second kind (fOU _ 2)(fOU 2) is a
solution of the Langevin equation d X_t=-θ X_t\, d t+ d Y_t^(1),\theta> 0 d X t=-θ X tdt+ d Y t …
solution of the Langevin equation d X_t=-θ X_t\, d t+ d Y_t^(1),\theta> 0 d X t=-θ X tdt+ d Y t …
Parameter estimation for a partially observed Ornstein–Uhlenbeck process with long-memory noise
B El Onsy, K Es-Sebaiy, F G. Viens - Stochastics, 2017 - Taylor & Francis
We consider the parameter estimation problem for the Ornstein–Uhlenbeck process X driven
by a fractional Ornstein–Uhlenbeck process V, ie the pair of processes defined by the non …
by a fractional Ornstein–Uhlenbeck process V, ie the pair of processes defined by the non …
Least squares estimator of fractional Ornstein–Uhlenbeck processes with periodic mean
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 …
(fOU) with periodic mean for every 1 2< H< 1. More precisely, we extend the consistency …
Parameter estimation for the Langevin equation with stationary-increment Gaussian noise
T Sottinen, L Viitasaari - Statistical Inference for Stochastic Processes, 2018 - Springer
We study the Langevin equation with stationary-increment Gaussian noise. We show the
strong consistency and the asymptotic normality with Berry–Esseen bound of the so-called …
strong consistency and the asymptotic normality with Berry–Esseen bound of the so-called …
Estimating drift parameters in a non-ergodic Gaussian Vasicek-type model
K Es-Sebaiy, M Es. Sebaiy - Statistical Methods & Applications, 2021 - Springer
We study a problem of parameter estimation for a non-ergodic Gaussian Vasicek-type model
defined as dX_t= θ (μ+ X_t) dt+ dG_t,\t ≥ 0 d X t= θ (μ+ X t) dt+ d G t, t≥ 0 with unknown …
defined as dX_t= θ (μ+ X_t) dt+ dG_t,\t ≥ 0 d X t= θ (μ+ X t) dt+ d G t, t≥ 0 with unknown …
Berry-Ess\'een bounds for parameter estimation of general Gaussian processes
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 …
general Gaussian sequences, using tools from analysis on Wiener space. No assumption of …
Asymptotic growth of trajectories of multifractional Brownian motion, with statistical applications to drift parameter estimation
M Dozzi, Y Kozachenko, Y Mishura… - Statistical inference for …, 2018 - Springer
We construct the least-square estimator for the unknown drift parameter in the multifractional
Ornstein–Uhlenbeck model and establish its strong consistency in the non-ergodic case …
Ornstein–Uhlenbeck model and establish its strong consistency in the non-ergodic case …
Self-normalized asymptotic properties for the parameter estimation in fractional Ornstein–Uhlenbeck process
H Jiang, J Liu, S Wang - Stochastics and Dynamics, 2019 - World Scientific
In this paper, we consider the self-normalized asymptotic properties of the parameter
estimators in the fractional Ornstein–Uhlenbeck process. The deviation inequalities, Cramér …
estimators in the fractional Ornstein–Uhlenbeck process. The deviation inequalities, Cramér …