Multifractional Brownian Motion with Telegraphic, Stochastically Varying Exponent

Abstract

The diversity of diffusive systems exhibiting long-range correlations characterized by a stochastically varying Hurst exponent calls for a generic multifractional model. We present a simple, analytically tractable model which fills the gap between mathematical formulations of multifractional Brownian motion and empirical studies. In our model, called telegraphic multifractional Brownian motion, the Hurst exponent is modeled by a smoothed telegraph process which results in a stationary beta distribution of exponents as observed in biological experiments. We also provide a methodology to identify our model in experimental data and present concrete examples from biology, climate, and finance to demonstrate the efficacy of our approach. Published by the American Physical Society 2025