On diffusion approximation of a slow component for solution of stochastic differential equation of Ito

TL;DR

This paper develops a diffusion approximation for the slow component of solutions to stochastic differential equations, providing a method to estimate the validity period of phenomenological diffusion laws in non-uniform environments.

Contribution

It introduces a new approach to estimate the time interval where Fick's laws accurately describe diffusion in stochastic systems.

Findings

Provides a method for time interval estimation of diffusion approximation

Enables assessment of phenomenological law validity in stochastic models

Applies to Brownian particles in non-uniform environments

Abstract

For the concrete model of Brownian particles dynamics in non-uniform environment, the time interval estimation is constructed, on which phenomenological Fick laws for diffusion phenomenon description can be used. The knowledge of these estimations gives the possibility to judge about adequacy of the initial assumption about dynamics of the real processes. Noted, that such an assessment has not been introduced yet, up to date.