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On construction, properties and simulation of Haar-based multifractional processes.

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Title: On construction, properties and simulation of Haar-based multifractional processes.
Authors: Ayache, Antoine1 (AUTHOR) antoine.ayache@univ-lille.fr, Olenko, Andriy1,2 (AUTHOR) A.Olenko@latrobe.edu.au, Samarakoon, Nemini1,2 (AUTHOR) n.wijesinghesamarakoon@latrobe.edu.au
Source: Mathematics & Computers in Simulation. Aug2026, Vol. 246, p311-332. 22p.
Subjects: Gaussian processes, Haar function, Stochastic processes, Stochastic models, Random noise theory, Simulation methods & models, Parameterization, Mathematical functions
Abstract: Multifractional processes extend the concept of fractional Brownian motion by replacing the constant Hurst parameter with a time-varying Hurst function. This allows to model systems with changing dynamic and to modulate the roughness of sample paths over time. The paper introduces a new class of multifractional processes, the Gaussian Haar-based multifractional processes (GHBMP), which is based on the Haar wavelet series representations. The resulting processes cover a significantly broader set of Hurst functions compared to the existing literature, enhancing their suitability for both practical applications and theoretical studies. The theoretical properties of these processes are investigated. It is demonstrated how the suggested representation of GHBMP can be easily implemented for simulations with various Hurst functions. The proposed model is validated and its applicability is demonstrated, even for Hurst functions exhibiting discontinuous behaviour. • A novel class of multifractional processes, GHBMP, is proposed. • GHBMP is based on the Haar wavelet series, resulting in efficient computation. • GHBMP can be used for a wide range of Hurst functions. • The paper examines key theoretical properties of GHBMP. • Simulations demonstrate applicability for various Hurst functions. [ABSTRACT FROM AUTHOR]
Copyright of Mathematics & Computers in Simulation is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: On construction, properties and simulation of Haar-based multifractional processes.
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  Data: <searchLink fieldCode="AR" term="%22Ayache%2C+Antoine%22">Ayache, Antoine</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> antoine.ayache@univ-lille.fr</i><br /><searchLink fieldCode="AR" term="%22Olenko%2C+Andriy%22">Olenko, Andriy</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> A.Olenko@latrobe.edu.au</i><br /><searchLink fieldCode="AR" term="%22Samarakoon%2C+Nemini%22">Samarakoon, Nemini</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> n.wijesinghesamarakoon@latrobe.edu.au</i>
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  Data: <searchLink fieldCode="JN" term="%22Mathematics+%26+Computers+in+Simulation%22">Mathematics & Computers in Simulation</searchLink>. Aug2026, Vol. 246, p311-332. 22p.
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  Data: <searchLink fieldCode="DE" term="%22Gaussian+processes%22">Gaussian processes</searchLink><br /><searchLink fieldCode="DE" term="%22Haar+function%22">Haar function</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+processes%22">Stochastic processes</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+models%22">Stochastic models</searchLink><br /><searchLink fieldCode="DE" term="%22Random+noise+theory%22">Random noise theory</searchLink><br /><searchLink fieldCode="DE" term="%22Simulation+methods+%26+models%22">Simulation methods & models</searchLink><br /><searchLink fieldCode="DE" term="%22Parameterization%22">Parameterization</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+functions%22">Mathematical functions</searchLink>
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  Data: Multifractional processes extend the concept of fractional Brownian motion by replacing the constant Hurst parameter with a time-varying Hurst function. This allows to model systems with changing dynamic and to modulate the roughness of sample paths over time. The paper introduces a new class of multifractional processes, the Gaussian Haar-based multifractional processes (GHBMP), which is based on the Haar wavelet series representations. The resulting processes cover a significantly broader set of Hurst functions compared to the existing literature, enhancing their suitability for both practical applications and theoretical studies. The theoretical properties of these processes are investigated. It is demonstrated how the suggested representation of GHBMP can be easily implemented for simulations with various Hurst functions. The proposed model is validated and its applicability is demonstrated, even for Hurst functions exhibiting discontinuous behaviour. • A novel class of multifractional processes, GHBMP, is proposed. • GHBMP is based on the Haar wavelet series, resulting in efficient computation. • GHBMP can be used for a wide range of Hurst functions. • The paper examines key theoretical properties of GHBMP. • Simulations demonstrate applicability for various Hurst functions. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Mathematics & Computers in Simulation is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.matcom.2026.01.033
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      – Code: eng
        Text: English
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        PageCount: 22
        StartPage: 311
    Subjects:
      – SubjectFull: Gaussian processes
        Type: general
      – SubjectFull: Haar function
        Type: general
      – SubjectFull: Stochastic processes
        Type: general
      – SubjectFull: Stochastic models
        Type: general
      – SubjectFull: Random noise theory
        Type: general
      – SubjectFull: Simulation methods & models
        Type: general
      – SubjectFull: Parameterization
        Type: general
      – SubjectFull: Mathematical functions
        Type: general
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      – TitleFull: On construction, properties and simulation of Haar-based multifractional processes.
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            NameFull: Ayache, Antoine
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            NameFull: Olenko, Andriy
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            NameFull: Samarakoon, Nemini
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            – D: 01
              M: 08
              Text: Aug2026
              Type: published
              Y: 2026
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              Value: 246
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