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

Author

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  • Ayache, Antoine
  • Olenko, Andriy
  • Samarakoon, Nemini

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.

Suggested Citation

  • Ayache, Antoine & Olenko, Andriy & Samarakoon, Nemini, 2026. "On construction, properties and simulation of Haar-based multifractional processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 246(C), pages 311-332.
    • Handle: RePEc:eee:matcom:v:246:y:2026:i:c:p:311-332
    DOI: 10.1016/j.matcom.2026.01.033
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