This paper addresses the problem of estimating the drift parameter of the Ornstein– Uhlenbeck-type process driven by the sum of independent standard and fractional Brownian motions. With the help of some recent results on the canonical representation and spectral structure of mixed processes, the maximum likelihood estimator is shown to be consistent and asymptotically normal in the large-sample limit.
Bibliographical noteFunding Information:
∗Received by the editors November 20, 2016; revised September 29, 2017. The work of the first author was supported by an ISF 558/13 grant. Originally published in the Russian journal Teoriya Veroyatnostei i ee Primeneniya, 63 (2018), pp. 500–519. http://www.siam.org/journals/tvp/63-3/T98914.html †Department of Statistics, The Hebrew University, Mount Scopus, Jerusalem, Israel (pchiga@ mscc.huji.ac.il). ‡Laboratoire Manceau de Mathématiques, Faculté des Sciences et Techniques, Universitédu Maine, France (email@example.com).
© 2019 Society for Industrial and Applied Mathematics.
- Fractional Brownian motion
- Maximum likelihood estimator
- Singularly perturbed integral equation
- Uhlenbeck process
- Weakly singular integral operator