Least squares estimator for non-ergodic Ornstein–Uhlenbeck processes driven by Gaussian processes
| Autor: | Youssef Ouknine, Khalifa Es-Sebaiy, Mohamed El Machkouri |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques Raphaël Salem (LMRS), Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS), Ecole Nationale des Sciences Appliquées [Marrakech] (ENSA), Faculté des Sciences Semlalia Marrakech |
| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
Hurst exponent Pure mathematics Fractional Brownian motion 010102 general mathematics Stochastic calculus Estimator Ornstein–Uhlenbeck process 01 natural sciences [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 010104 statistics & probability symbols.namesake Mathematics::Probability symbols Ergodic theory 0101 mathematics Gaussian process ComputingMilieux_MISCELLANEOUS Brownian motion Mathematics |
| Zdroj: | Journal of the Korean Statistical Society Journal of the Korean Statistical Society, Elsevier, 2016, 45 (3), pp.329-341. ⟨10.1016/j.jkss.2015.12.001⟩ |
| ISSN: | 1226-3192 |
| DOI: | 10.1016/j.jkss.2015.12.001 |
| Popis: | 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 models. In the present paper we consider the drift parameter estimation problem for the non-ergodic Ornstein–Uhlenbeck process defined as d X t = θ X t d t + d G t , t ≥ 0 with an unknown parameter θ > 0 , where G is a Gaussian process. We provide sufficient conditions, based on the properties of G , ensuring the strong consistency and the asymptotic distribution of our estimator θ ˜ t of θ based on the observation { X s , s ∈ [ 0 , t ] } as t → ∞ . Our approach offers an elementary, unifying proof of Belfadli (2011), and it allows to extend the result of Belfadli (2011) to the case when G is a fractional Brownian motion with Hurst parameter H ∈ ( 0 , 1 ) . We also discuss the cases of subfractional Brownian motion and bifractional Brownian motion. |
| Databáze: | OpenAIRE |
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