Parameter estimation for the complex fractional Ornstein–Uhlenbeck processes with Hurst parameter H∈(0,12)

We study the strong consistency and asymptotic normality of a least squares estimator of the drift coefficient in complex-valued Ornstein–Uhlenbeck processes driven by fractional Brownian motion, extending the results of Chen et al. (2017) to the case of Hurst parameter H∈(14,12) and the results of...

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Published inChaos, solitons and fractals Vol. 188; p. 115556
Main Authors Alazemi, Fares, Alsenafi, Abdulaziz, Chen, Yong, Zhou, Hongjuan
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.11.2024
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Abstract We study the strong consistency and asymptotic normality of a least squares estimator of the drift coefficient in complex-valued Ornstein–Uhlenbeck processes driven by fractional Brownian motion, extending the results of Chen et al. (2017) to the case of Hurst parameter H∈(14,12) and the results of Hu et al. (2019) to a two-dimensional case. When H∈(0,14], it is found that the integrand of the estimator is not in the domain of the standard divergence operator. To facilitate the proofs, we develop a new inner product formula for functions of bounded variation in the reproducing kernel Hilbert space of fractional Brownian motion with Hurst parameter H∈(0,12). This formula is also applied to obtain the second moments of the so-called α-order fractional Brownian motion and the α-fractional bridges with the Hurst parameter H∈(0,12). •We develop a new inner product formula for functions in the reproducing kernel Hilbert space of fBm.•We prove the asymptotics for the LS estimator of the drift coefficient in complex fOU processes.•We estimate the second moments of the α-order fBm and the α-fractional bridges.
AbstractList We study the strong consistency and asymptotic normality of a least squares estimator of the drift coefficient in complex-valued Ornstein–Uhlenbeck processes driven by fractional Brownian motion, extending the results of Chen et al. (2017) to the case of Hurst parameter H∈(14,12) and the results of Hu et al. (2019) to a two-dimensional case. When H∈(0,14], it is found that the integrand of the estimator is not in the domain of the standard divergence operator. To facilitate the proofs, we develop a new inner product formula for functions of bounded variation in the reproducing kernel Hilbert space of fractional Brownian motion with Hurst parameter H∈(0,12). This formula is also applied to obtain the second moments of the so-called α-order fractional Brownian motion and the α-fractional bridges with the Hurst parameter H∈(0,12). •We develop a new inner product formula for functions in the reproducing kernel Hilbert space of fBm.•We prove the asymptotics for the LS estimator of the drift coefficient in complex fOU processes.•We estimate the second moments of the α-order fBm and the α-fractional bridges.
ArticleNumber 115556
Author Zhou, Hongjuan
Alazemi, Fares
Chen, Yong
Alsenafi, Abdulaziz
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  organization: Department of Mathematics, Faculty of Science, Kuwait University, Kuwait
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  organization: School of Mathematical and Statistical Sciences, Arizona State University, Tempe, 85287, AZ, USA
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Cites_doi 10.1007/s10473-021-0218-x
10.1080/17442508.2021.1959587
10.30757/ALEA.v14-30
10.1080/17442508.2018.1563606
10.1007/s440-000-8016-7
10.1007/s13171-021-00266-z
10.1016/j.jmaa.2006.07.100
10.1007/s11203-017-9168-2
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Keywords 60G22
α-fractional Brownian bridge
62M09
Least squares estimate
Complex Wiener–Itô multiple integral
Fractional Brownian motion
α-order fractional Brownian motion
60G15
Fractional Ornstein–Uhlenbeck process
Fourth moment theorem
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References Carter (b16) 1958; 65
Wheeden, Zygmund (b13) 1977
Chen, Chen, Liu (b15) 2024
Chen, Hu, Wang (b4) 2017; 14
Hu, Nualart, Zhou (b6) 2019; 22
Pipiras, Taqqu (b17) 2000; 118
Chen, Gao, Li (b11) 2024
Es-Sebaiy, Nourdin (b8) 2013
Chen, Zhou (b18) 2021; 41B
Mishura (b9) 2008
El Omari (b7) 2023; 85
Folland (b12) 1999; vol. 40
Shen, Tang, Yin (b5) 2022; 94
Hu, Nualart, Zhou (b1) 2019; 91
Jolis (b10) 2007; 330
Reed, Simon (b14) 1980
Arató (b3) 1982; vol. 45
Arató, Kolmogorov, Sinai (b2) 1962; 146
Chen (10.1016/j.chaos.2024.115556_b4) 2017; 14
Folland (10.1016/j.chaos.2024.115556_b12) 1999; vol. 40
Reed (10.1016/j.chaos.2024.115556_b14) 1980
Mishura (10.1016/j.chaos.2024.115556_b9) 2008
Chen (10.1016/j.chaos.2024.115556_b15) 2024
Carter (10.1016/j.chaos.2024.115556_b16) 1958; 65
El Omari (10.1016/j.chaos.2024.115556_b7) 2023; 85
Chen (10.1016/j.chaos.2024.115556_b18) 2021; 41B
Arató (10.1016/j.chaos.2024.115556_b3) 1982; vol. 45
Wheeden (10.1016/j.chaos.2024.115556_b13) 1977
Pipiras (10.1016/j.chaos.2024.115556_b17) 2000; 118
Hu (10.1016/j.chaos.2024.115556_b6) 2019; 22
Chen (10.1016/j.chaos.2024.115556_b11) 2024
Shen (10.1016/j.chaos.2024.115556_b5) 2022; 94
Jolis (10.1016/j.chaos.2024.115556_b10) 2007; 330
Hu (10.1016/j.chaos.2024.115556_b1) 2019; 91
Arató (10.1016/j.chaos.2024.115556_b2) 1962; 146
Es-Sebaiy (10.1016/j.chaos.2024.115556_b8) 2013
References_xml – volume: 118
  start-page: 251
  year: 2000
  end-page: 291
  ident: b17
  article-title: Integration questions related to fractional Brownian motion
  publication-title: Probab Theory Related Fields
  contributor:
    fullname: Taqqu
– volume: 22
  start-page: 111
  year: 2019
  end-page: 142
  ident: b6
  article-title: Parameter estimation for fractional Ornstein–Uhlenbeck processes of general Hurst parameter
  publication-title: Stat Inference Stoch Process
  contributor:
    fullname: Zhou
– year: 2008
  ident: b9
  article-title: Stochastic calculus for fractional Brownian motion and related processes
  contributor:
    fullname: Mishura
– volume: 94
  start-page: 537
  year: 2022
  end-page: 558
  ident: b5
  article-title: Least-squares estimation for the Vasicek model driven by the complex fractional Brownian motion
  publication-title: Stochastics
  contributor:
    fullname: Yin
– volume: 85
  start-page: 572
  year: 2023
  end-page: 599
  ident: b7
  article-title: An
  publication-title: Sankhya A
  contributor:
    fullname: El Omari
– year: 1980
  ident: b14
  article-title: Methods of modern mathematical physics
  publication-title: Volume I: functional analysis
  contributor:
    fullname: Simon
– volume: 91
  start-page: 1067
  year: 2019
  end-page: 1091
  ident: b1
  article-title: Drift parameter estimation for nonlinear stochastic differential equations driven by fractional Brownian motion
  publication-title: Stochastics
  contributor:
    fullname: Zhou
– year: 2024
  ident: b11
  article-title: Statistical estimations for non-ergodic vasicek model driven by two types of Gaussian processes
  contributor:
    fullname: Li
– year: 2024
  ident: b15
  article-title: Berry-Esséen bound for complex Wiener-Itô integral
  contributor:
    fullname: Liu
– year: 1977
  ident: b13
  article-title: Measure and integral
  contributor:
    fullname: Zygmund
– volume: 146
  start-page: 747
  year: 1962
  end-page: 750
  ident: b2
  article-title: An estimate of the parameters of a complex stationary Gaussian Markov process
  publication-title: Dokl Akad Nauk SSSR
  contributor:
    fullname: Sinai
– volume: 41B
  start-page: 573
  year: 2021
  end-page: 595
  ident: b18
  article-title: Parameter estimation for an Ornstein–Uhlenbeck processes driven by a general Gaussian noise
  publication-title: Acta Math Sci
  contributor:
    fullname: Zhou
– volume: vol. 40
  year: 1999
  ident: b12
  publication-title: Real analysis
  contributor:
    fullname: Folland
– volume: vol. 45
  year: 1982
  ident: b3
  article-title: Linear stochastic systems with constant coefficients
  publication-title: A statistical approach
  contributor:
    fullname: Arató
– volume: 14
  start-page: 613
  year: 2017
  end-page: 629
  ident: b4
  article-title: Parameter estimation of complex fractional Ornstein–Uhlenbeck processes with fractional noise
  publication-title: ALEA Lat Am J Probab Math Stat
  contributor:
    fullname: Wang
– volume: 330
  start-page: 1115
  year: 2007
  end-page: 1127
  ident: b10
  article-title: On the Wiener integral with respect to the fractional Brownian motion on an interval
  publication-title: J Math Anal Appl
  contributor:
    fullname: Jolis
– volume: 65
  start-page: 264
  year: 1958
  end-page: 266
  ident: b16
  article-title: L’Hospital’s rule for complex-valued functions
  publication-title: Appl Math Model
  contributor:
    fullname: Carter
– start-page: 385
  year: 2013
  end-page: 412
  ident: b8
  article-title: Parameter estimation for
  publication-title: Malliavin calculus and stochastic analysis
  contributor:
    fullname: Nourdin
– volume: 41B
  start-page: 573
  issue: 2
  year: 2021
  ident: 10.1016/j.chaos.2024.115556_b18
  article-title: Parameter estimation for an Ornstein–Uhlenbeck processes driven by a general Gaussian noise
  publication-title: Acta Math Sci
  doi: 10.1007/s10473-021-0218-x
  contributor:
    fullname: Chen
– year: 1980
  ident: 10.1016/j.chaos.2024.115556_b14
  article-title: Methods of modern mathematical physics
  contributor:
    fullname: Reed
– start-page: 385
  year: 2013
  ident: 10.1016/j.chaos.2024.115556_b8
  article-title: Parameter estimation for α-fractional bridges
  contributor:
    fullname: Es-Sebaiy
– volume: 146
  start-page: 747
  year: 1962
  ident: 10.1016/j.chaos.2024.115556_b2
  article-title: An estimate of the parameters of a complex stationary Gaussian Markov process
  publication-title: Dokl Akad Nauk SSSR
  contributor:
    fullname: Arató
– volume: 94
  start-page: 537
  issue: 4
  year: 2022
  ident: 10.1016/j.chaos.2024.115556_b5
  article-title: Least-squares estimation for the Vasicek model driven by the complex fractional Brownian motion
  publication-title: Stochastics
  doi: 10.1080/17442508.2021.1959587
  contributor:
    fullname: Shen
– year: 2024
  ident: 10.1016/j.chaos.2024.115556_b15
  contributor:
    fullname: Chen
– year: 1977
  ident: 10.1016/j.chaos.2024.115556_b13
  contributor:
    fullname: Wheeden
– volume: 14
  start-page: 613
  year: 2017
  ident: 10.1016/j.chaos.2024.115556_b4
  article-title: Parameter estimation of complex fractional Ornstein–Uhlenbeck processes with fractional noise
  publication-title: ALEA Lat Am J Probab Math Stat
  doi: 10.30757/ALEA.v14-30
  contributor:
    fullname: Chen
– year: 2024
  ident: 10.1016/j.chaos.2024.115556_b11
  contributor:
    fullname: Chen
– volume: 65
  start-page: 264
  issue: 4
  year: 1958
  ident: 10.1016/j.chaos.2024.115556_b16
  article-title: L’Hospital’s rule for complex-valued functions
  publication-title: Appl Math Model
  contributor:
    fullname: Carter
– volume: vol. 40
  year: 1999
  ident: 10.1016/j.chaos.2024.115556_b12
  contributor:
    fullname: Folland
– volume: 91
  start-page: 1067
  issue: 8
  year: 2019
  ident: 10.1016/j.chaos.2024.115556_b1
  article-title: Drift parameter estimation for nonlinear stochastic differential equations driven by fractional Brownian motion
  publication-title: Stochastics
  doi: 10.1080/17442508.2018.1563606
  contributor:
    fullname: Hu
– year: 2008
  ident: 10.1016/j.chaos.2024.115556_b9
  contributor:
    fullname: Mishura
– volume: vol. 45
  year: 1982
  ident: 10.1016/j.chaos.2024.115556_b3
  article-title: Linear stochastic systems with constant coefficients
  contributor:
    fullname: Arató
– volume: 118
  start-page: 251
  issue: 2
  year: 2000
  ident: 10.1016/j.chaos.2024.115556_b17
  article-title: Integration questions related to fractional Brownian motion
  publication-title: Probab Theory Related Fields
  doi: 10.1007/s440-000-8016-7
  contributor:
    fullname: Pipiras
– volume: 85
  start-page: 572
  issue: 1
  year: 2023
  ident: 10.1016/j.chaos.2024.115556_b7
  article-title: An α-order fractional Brownian motion with hurst index H∈(0,1) and α∈R+
  publication-title: Sankhya A
  doi: 10.1007/s13171-021-00266-z
  contributor:
    fullname: El Omari
– volume: 330
  start-page: 1115
  issue: 2
  year: 2007
  ident: 10.1016/j.chaos.2024.115556_b10
  article-title: On the Wiener integral with respect to the fractional Brownian motion on an interval
  publication-title: J Math Anal Appl
  doi: 10.1016/j.jmaa.2006.07.100
  contributor:
    fullname: Jolis
– volume: 22
  start-page: 111
  year: 2019
  ident: 10.1016/j.chaos.2024.115556_b6
  article-title: Parameter estimation for fractional Ornstein–Uhlenbeck processes of general Hurst parameter
  publication-title: Stat Inference Stoch Process
  doi: 10.1007/s11203-017-9168-2
  contributor:
    fullname: Hu
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Snippet We study the strong consistency and asymptotic normality of a least squares estimator of the drift coefficient in complex-valued Ornstein–Uhlenbeck processes...
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StartPage 115556
SubjectTerms Complex Wiener–Itô multiple integral
Fourth moment theorem
Fractional Brownian motion
Fractional Ornstein–Uhlenbeck process
Least squares estimate
α-fractional Brownian bridge
α-order fractional Brownian motion
Title Parameter estimation for the complex fractional Ornstein–Uhlenbeck processes with Hurst parameter H∈(0,12)
URI https://dx.doi.org/10.1016/j.chaos.2024.115556
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