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Teor. Veroyatnost. i Primenen., 2018, Volume 63, Issue 3, Pages 500–519 (Mi tvp5178)  

Statistical analysis of the mixed fractional Ornstein–Uhlenbeck process

P. Chiganskya, M. Kleptsynab

a Department of Statistics, The Hebrew University, Mount Scopus, Jerusalem, Israel
b Laboratoire Manceau de Mathématiques, Faculté des Sciences et Techniques, Université du Maine, France

Abstract: 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.

Keywords: maximum likelihood estimator, Ornstein–Uhlenbeck process, fractional Brownian motion, singularly perturbed integral equation, weakly singular integral operator.

Funding Agency Grant Number
Israel Science Foundation 558/13
P. Chigansky is supported by ISF 558/13 grant.


DOI: https://doi.org/10.4213/tvp5178

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English version:
Theory of Probability and its Applications, 2019, 63:3, 408–425

Bibliographic databases:

Received: 20.09.2016
Revised: 29.10.2017
Accepted:23.12.2017
Language:

Citation: P. Chigansky, M. Kleptsyna, “Statistical analysis of the mixed fractional Ornstein–Uhlenbeck process”, Teor. Veroyatnost. i Primenen., 63:3 (2018), 500–519; Theory Probab. Appl., 63:3 (2019), 408–425

Citation in format AMSBIB
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