Anomalous diffusion for overdamped particles driven by cross-correlated white noise sources

TL;DR

This paper investigates the statistical behavior of overdamped particles influenced by cross-correlated white noises, deriving exact distributions and classifying their anomalous diffusion regimes in time-dependent environments.

Contribution

It provides exact probability distributions and long-time behavior analysis for particles driven by correlated noises, advancing understanding of anomalous diffusion in stochastic systems.

Findings

Derived exact probability distribution functions.

Classified various anomalous diffusion regimes.

Confirmed asymptotic behaviors with explicit examples.

Abstract

We study the statistical properties of overdamped particles driven by two cross-correlated multiplicative Gaussian white noises in a time-dependent environment. Using the Langevin and Fokker-Planck approaches, we derive the exact probability distribution function for the particle positions, calculate its moments and find their corresponding long-time, asymptotic behaviors. The generally anomalous diffusive regimes of the particles are classified, and their dependence on the friction coefficient and the characteristics of the noises is analyzed in detail. The asymptotic predictions are confirmed by exact solutions for two examples.