Title :

Least squares estimator for the parameter of the fractional Ornstein-Uhlenbeck sheet

Author(s) :

Clarke de La Cerda, Jorge [Auteur]
Tudor, Ciprian [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Journal of the Korean Statistical Society

Pages :

341 - 350

Publisher :

Elsevier

Publication date :

2012

ISSN :

1226-3192

English keyword(s) :

Multiple Wiener–Itô integrals
Strong consistency
Fractional Brownian sheet
Parameter estimation

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]
Statistiques [stat]

English abstract : [en]

We will study the least square estimator $\widehat{\theta }_{T,S}$ for the drift parameter $\theta$ of the fractional Ornstein-Uhlenbeck sheet which is defined as the solution of the Langevin equation \begin{equation*} ...
Show more >We will study the least square estimator $\widehat{\theta }_{T,S}$ for the drift parameter $\theta$ of the fractional Ornstein-Uhlenbeck sheet which is defined as the solution of the Langevin equation \begin{equation*} X_{t,s}= -\theta \int^{t}_{0} \int^{s}_{0} X_{v,u}dvdu + B^{\alpha, \beta}_{t,s}, \qquad (t,s) \in [0,T]\times [0,S]. \end{equation*} driven by the fractional Brownian sheet $B^{\alpha ,\beta}$ with Hurst parameters $\alpha, \beta$ in $(\frac{1}{2}, \frac{5}{8})$. Using the properties of multiple Wiener-Itô integrals we prove that the estimator is strongly consistent for the parameter $\theta$. In contrast to the one-dimensional case, the estimator $\widehat{\theta}_{T,S}$ is not asymptotically normal.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL