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Non-Gaussian behavior in fractional Laplace motion with drift.
Wei Wang1, Yingjie Liang1,2, Aleksei V Chechkin1,3,4,5
1University of Potsdam, Institute of Physics and Astronomy, 14476 Potsdam, Germany.
Physical Review. E
|April 18, 2025
Summary
We explore fractional Laplace motion (FLM) and its statistical properties. Internal drift causes normal diffusion and breaks PDF symmetry, while external drift preserves it, offering insights into complex stochastic processes.
Area of Science:
- Stochastic Processes
- Statistical Physics
- Mathematical Physics
Background:
- Fractional Brownian motion (FBM) describes anomalous diffusion.
- Subordination of FBM to a gamma process yields fractional Laplace motion (FLM).
- Drift forces significantly alter stochastic process dynamics.
Purpose of the Study:
- Investigate statistical properties of FLM with external and internal drifts.
- Analyze the impact of drifts on mean-squared displacement and probability density function (PDF).
- Determine the suitability of FLM for modeling non-Gaussian processes.
Main Methods:
- Theoretical derivation of FLM statistical properties.
- Analysis of mean-squared displacement and PDF behavior under different drift conditions.
- Comparison of theoretical predictions with computer simulations.
Main Results:
- External drift does not affect mean-squared displacement; internal drift induces normal diffusion.
- FLM exhibits a central Gaussian PDF region and non-Gaussian tails, influenced by FBM's Hurst exponent.
- Internal drift breaks PDF symmetry, while external drift maintains it.
Conclusions:
- FLM models stochastic processes with non-Gaussian PDFs and long-range correlations.
- Drift type critically influences FLM's diffusive behavior and symmetry.
- Simulations confirm theoretical predictions, validating the FLM model.
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