Memory-multi-fractional Brownian motion with continuous correlations

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 changing environment. In MMFBM built-in, long-range is continuously modulated by α(t). derive essential statistical properties such as its response function, mean-squared displacement (MSD), autocovariance and Gaussian distribution. contrast existing forms FBM time-varying exponents but reset structure, instantaneous dynamic influenced process history, e.g., we show that after steplike change scaling MSD α step may be determined value before change. versatile useful for correlated physical systems nonequilibrium initial conditions environment.Received 9 October 2022Accepted 14 July 2023DOI:https://doi.org/10.1103/PhysRevResearch.5.L032025Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution this work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasAnomalous diffusionFractional motionIntracellular transportInterdisciplinary PhysicsBiological PhysicsStatistical Physics