2025/04/20 by Michał Balcerek, Balcerek, Michał, Samudrajit Thapa +13 · 1 voice · 1 citation
Economics, Econometrics and Finance · Environmental Science · Physics and Astronomy · #Complex Systems and Time Series Analysis #Ecosystem dynamics and resilience #Statistical Mechanics and Entropy
paper · pdf · doi:10.1103/physrevlett.134.197101
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.