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This study provides accurate approximations for the mean and variance of reflected fractional Brownian motion, a key process for modeling anomalous diffusion. These findings offer a practical solution where exact methods are unavailable.

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Area of Science:

  • Stochastic processes
  • Anomalous diffusion modeling

Background:

  • Fractional Brownian motion (fBm) is essential for modeling anomalous diffusion.
  • Accurate characterization of reflected fBm is challenging due to limitations in explicit expressions and numerical techniques.

Purpose of the Study:

  • To derive accurate approximations for the mean and variance of fractional Brownian motion reflected at level 0.
  • To provide practical tools for analyzing reflected fBm in scenarios lacking direct analytical solutions.

Main Methods:

  • Utilized Monte Carlo simulation as the primary analytical approach.
  • Developed and validated closed-form approximations based on simulation data.

Main Results:

  • Achieved closed-form approximations for the mean and variance of reflected fractional Brownian motion.
  • Demonstrated a near-perfect fit between the approximations and simulation results.

Conclusions:

  • The proposed closed-form approximations offer a reliable and efficient method for estimating the mean and variance of reflected fractional Brownian motion.
  • These findings enhance the ability to model and analyze anomalous diffusion processes in various scientific and engineering fields.