Affiliation:
1. National School of Applied Sciences-Marrakesh , Cadi Ayyad University , Marrakesh , Morocco
Abstract
Abstract
We consider a problem of parameter estimation for the fractional Ornstein–Uhlenbeck model given by the stochastic differential equation
d
X
t
=
-
θ
X
t
d
t
+
d
B
t
H
{dX_{t}=-\theta X_{t}dt+dB_{t}^{H}}
,
t
≥
0
{t\geq 0}
, where
θ
>
0
{\theta>0}
is an unknown parameter to be estimated and
B
H
{B^{H}}
is a fractional Brownian motion with Hurst parameter
H
∈
(
0
,
1
)
{H\in(0,1)}
. We provide an estimator for θ, and then we study its strong consistency and asymptotic normality. The main tool in our proofs is the paper
[I. Nourdin, D. Nualart and G. Peccati,
The Breuer–Major theorem in total variation: Improved rates under minimal regularity,
Stochastic Process. Appl. 131 2021, 1–20].
Subject
Statistics and Probability,Analysis
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