Statistical analysis of the mixed fractional Ornstein–Uhlenbeck process

P. Chigansky; M. Kleptsyna

doi:10.1137/S0040585X97T989143

Statistical analysis of the mixed fractional Ornstein–Uhlenbeck process

P. Chigansky, M. Kleptsyna

Department of Statistics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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.

Original language	American English
Pages (from-to)	408-425
Number of pages	18
Journal	Theory of Probability and its Applications
Volume	63
Issue number	3
DOIs	https://doi.org/10.1137/S0040585X97T989143
State	Published - 2019

Bibliographical note

Funding 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 (marina.kleptsyna@univ-lemans.fr).

Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics.

Keywords

Fractional Brownian motion
Maximum likelihood estimator
Ornstein
Singularly perturbed integral equation
Uhlenbeck process
Weakly singular integral operator

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10.1137/S0040585X97T989143

Cite this

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title = "Statistical analysis of the mixed fractional Ornstein–Uhlenbeck process",

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 = "Fractional Brownian motion, Maximum likelihood estimator, Ornstein, Singularly perturbed integral equation, Uhlenbeck process, Weakly singular integral operator",

author = "P. Chigansky and M. Kleptsyna",

note = "Funding 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 Math{\'e}matiques, Facult{\'e} des Sciences et Techniques, Universit{\'e}du Maine, France (marina.kleptsyna@univ-lemans.fr). Publisher Copyright: {\textcopyright} 2019 Society for Industrial and Applied Mathematics.",

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AU - Kleptsyna, M.

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N2 - 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.

AB - 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.

KW - Fractional Brownian motion

KW - Maximum likelihood estimator

KW - Ornstein

KW - Singularly perturbed integral equation

KW - Uhlenbeck process

KW - Weakly singular integral operator

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DO - 10.1137/S0040585X97T989143

M3 - Article

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SN - 0040-585X

VL - 63

SP - 408

EP - 425

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

IS - 3

ER -

Statistical analysis of the mixed fractional Ornstein–Uhlenbeck process

Abstract

Bibliographical note

Keywords

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