2023/03/02 by Wang, Wei, Balcerek, Michal, Burnecki, Krzysztof +6
#Biological Physics (physics.bio-ph) #FOS: Biological sciences #FOS: Physical sciences #Quantitative Methods (q-bio.QM) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2303.01551
We propose a generalization of the widely used fractional Brownian motion (FBM), memory-multi-FBM (MMFBM), to describe viscoelastic or persistent anomalous diffusion with time-dependent memory exponent α(t) in a changing environment. In MMFBM the built-in, long-range memory is continuously modulated by α(t). We derive the essential statistical properties of MMFBM such as response function, mean-squared displacement (MSD), autocovariance function, and Gaussian distribution. In contrast to existing forms of FBM with time-varying memory exponents but reset memory structure, the instantaneous dynamic of MMFBM is influenced by the process history, e.g., we show that after a step-like change of α(t) the scaling exponent of the MSD after the α-step may be determined by the value of α(t) before the change. MMFBM is a versatile and useful process for correlated physical systems with non-equilibrium initial conditions in a changing environment.