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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]
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Database: Engineering Source
Description
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]
ISSN:03784754
DOI:10.1016/j.matcom.2026.01.033