Riemann-Liouville fractional Brownian motion with random Hurst exponent

Area of Science:

• Stochastic processes
• Anomalous diffusion
• Mathematical biology

Background:

• Standard Gaussian models with fixed parameters inadequately describe biological data exhibiting long-range dependence.
• Random parameters are introduced to enhance stochastic models for biological applications.
• Fractional Brownian motion with random Hurst exponent (FBMRE) is a recently studied model.

Purpose of the Study:

• To investigate the unexplored Riemann-Liouville fractional Brownian motion with random exponent (RL FBMRE).
• To compare the probabilistic properties of RL FBMRE with FBMRE.
• To advance the theory of doubly stochastic anomalous diffusion models.

Main Methods:

• Analysis of autocovariance functions and time-averaged mean squared displacement.
• Examination of the second moment of increment processes.
• Investigation of ergodicity properties and asymptotic behavior.

Main Results:

• Key differences in probabilistic properties and asymptotic behavior between RL FBMRE and FBMRE were identified.
• The study provides a theoretical foundation for distinguishing between these two complex stochastic processes.
• Characterization of anomalous diffusion behavior in models with random parameters.

Conclusions:

• RL FBMRE presents distinct characteristics compared to FBMRE, particularly in its asymptotic behavior.
• The theoretical framework developed can aid in parameter estimation from experimental data.
• This research contributes to a deeper understanding of complex diffusion phenomena in biological systems.