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Ayache, A. and Vehel, J.L. (2000) The Generalized Multifractional Brownian Motion. Statistical Inference for Stochastic Processes, 3, 7-18.
https://doi.org/10.1023/a:1009901714819

has been cited by the following article:

• TITLE: Application of Multifractional Brownian Motion to Modeling Volatility and Risk in Financial Markets

  AUTHORS: Bou Diop

  KEYWORDS: Multifractional Brownian Motion (mBm), Hurst Exponent, Volatility Modeling, Long Memory, Financial Risk, Stochastic Volatility, Value at Risk (VaR), Expected Shortfall (ES), Time-Varying Regularity

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.11, November 17, 2025

  ABSTRACT: This article proposes an innovative method for modeling financial markets using multifractional Brownian motion (mBm). Unlike traditional fractional Brownian motion, mBm offers variable local memory, providing a more accurate representation of the multifractal volatility and long-range dependencies found in financial time series. We present a precise mathematical formulation of mBm, sophisticated techniques for estimating the Hurst function, efficient numerical simulation algorithms, and a detailed empirical study covering several major stock indices. The results indicate that mBm more accurately reflects price dynamics, significantly improves risk analysis, and provides more precise pricing of exotic options compared to traditional models.