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 …

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 …

Abstract Generalizations of the Ornstein–Uhlenbeck process defined through Langevin
equations, such as fractional Ornstein–Uhlenbeck processes, have recently received a lot of …

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 …

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 …

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 …

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 …

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 asymptotic properties of the minimum-contrast estimators of the
drift parameter in linear stochastic evolution equations driven by fractional Brownian motion …

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 …